@article{
	11589_5939,
	author = { BYUN S -S  and  PALAGACHEV D K  and  SOFTOVA L G },
	title = {Global gradient estimates 
in weighted Lebesgue spaces
for parabolic operators},
	year = {2016},
	journal = {ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA},
	volume = {41},
	abstract = {We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with
measurable data over non-smooth domains,
related to variational problems arising in the modeling of composite materials and in the mechanics of membranes and films of simple non-homogeneous materials which form a linear laminated medium.
Assuming partial BMO smallness of the coefficients
 and Reifenberg flatness of the boundary of the underlying domain, we develop
a Calder\'{o}n--Zygmund type theory for such parabolic operators in the settings of the
weighted Lebesgue spaces. 
As consequence of the main result, we get regularity 
in parabolic Morrey scales for the spatial gradient of the weak solutions to the problems considered.},
	keywords = {Weighted Lebesgue space; Muckenhoupt weight; Parabolic system; Measurable coefficients; Gradient estimates; Morrey space},
	doi = {10.5186/aasfm.2016.4102},	
	pages = {67--83}
}
@article{
	11589_1692,
	author = { BYUN S -S  and  OK J  and  PALAGACHEV D K  and  SOFTOVA L G },
	title = {Parabolic systems with measurable coefficients in weighted Orlicz spaces},
	year = {2016},
	journal = {COMMUNICATIONS IN CONTEMPORARY MATHEMATICS},
	volume = {18},
	abstract = {We consider a parabolic system in divergence form with measurable
coefficients in a non-smooth bounded domain when the associated nonhomogeneous term belongs to a weighted Orlicz space.
We generalize the Calder\'{o}n-Zygmund theorem for the weak solution of such a
system as an optimal estimate in weighted Orlicz spaces, by essentially proving that the spatial gradient is as integrable as the nonhomogeneous term
under a possibly optimal assumption on the coefficients and a minimal geometric assumption on the boundary of the domain.},
	keywords = {Parabolic system; Measurable coefficients; Muckenhoupt weight; Orlicz space; Reifenberg domains; BMO},
	url = {http://www.worldscientific.com/doi/abs/10.1142/S0219199715500182},
	doi = {10.1142/S0219199715500182},	
	pages = {1--19}
}
@article{
	11589_59921,
	author = { Byun  Sun-Sig  and  Lee  Mikyoung  and  Palagachev  Dian K },
	title = {Hessian estimates in weighted Lebesgue spaces for fully nonlinear elliptic equations},
	year = {2016},
	journal = {JOURNAL OF DIFFERENTIAL EQUATIONS},
	volume = {260},
	abstract = {We prove global regularity in weighted Lebesgue spaces for the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equations. As a consequence, regularity in Morrey spaces of the Hessian is derived as well.},
	keywords = {Fully nonlinear equation; Hessian estimates; Morrey space; Muckenhoupt weight; Viscosity solution; Weighted Lebesgue space},
	url = {http://www.sciencedirect.com/science/article/pii/S0022039615006312},
	doi = {10.1016/j.jde.2015.11.025},	
	pages = {4550--4571}
}
@article{
	11589_6908,
	author = { BYUN S -S  and  CHO Y  and  PALAGACHEV D K },
	title = {Global weighted estimates for nonlinear elliptic obstacle problems over Reifenberg domains},
	year = {2015},
	journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
	volume = {143},
	abstract = {We study the obstacle problem for an elliptic equation with discontinuous nonlinearity over a nonsmooth domain, assuming that the irregular obstacle
and the nonhomogeneous term belong to
suitable weighted Sobolev and Lebesgue spaces, respectively,  with  weights taken in the Muckenhoupt classes. We establish a Calder\'{o}n--Zygmund type result by proving
that the gradient of the weak solution to the nonlinear obstacle problem has the same weighted integrability as both the gradient of the obstacle and the nonhomogeneous term, provided that the nonlinearity has a small BMO-semi norm with respect to the gradient and the boundary of the domain is $\delta$-Reifenberg flat. As consequence, we get global regularity in the settings of the Morrey and H\"older spaces for the weak solutions to the problem considered.},
	keywords = {Nonlinear elliptic equation; Obstacle problem; Irregular obstacle; Calder\'{o}n-Zygmund estimate; Muckenhoupt weight; $p$-Laplacean; BMO; Reifenberg flat domain; Morrey space},
	url = {http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2015-12458-6/},
	doi = {10.1090/S0002-9939-2015-12458-6},	
	pages = {2527--2541}
}
@article{
	11589_5782,
	author = { BYUN S -S  and  PALAGACHEV D K  and  SHIN  and  P },
	title = {Global continuity of solutions to quasilinear equations with Morrey data},
	year = {2015},
	journal = {COMPTES RENDUS MATHEMATIQUE},
	volume = {353},
	abstract = {We announce some recent results on boundedness and Hoelder continuity up to the boundary for the weak solutions
to coercive quasilinear equations with data belonging to Morrey spaces.},
	url = {http://www.sciencedirect.com/science/article/pii/S1631073X15001570},
	doi = {10.1016/j.crma.2015.06.003},	
	pages = {717--721}
}
@conference{
	11589_18312,
	author = { PALAGACHEV D K  and  BYUN S -S  and  SHIN  and  P },
	title = {Global Hölder continuity of weak solutions to
quasilinear elliptic equations with Morrey data},
	year = {2014},
	publisher = {Gangemi editore},
	address = {Roma},
	volume = {C2},
	booktitle = {Contributi di Ricerca 2 - Research Contributions 2
1° Workshop sullo stato dell'arte delle ricerche nel Politecnico di Bari – 1st Workshop on the State of the Art and Challenges of Research Efforts at POLIBA},
	abstract = {The note deals with solutions to the Dirichlet problem for general
quasilinear divergence-form elliptic operators whose prototype is the p-Laplacean
operator. The nonlinear terms are given by Carathéodory functions and
satisfy the natural structure conditions of Ladyzhenskaya and Ural’tseva with
data belonging to suitable Morrey spaces. The fairly non-regular boundary of
the underlying domain is supposed to satisfy a capacity density condition which
allows domains with exterior cone (or even corkscrew) property.
We prove Hölder continuity up to the boundary for the boundedweak solutions
of such equations, generalizing thisway the classical L^p -result of Ladyzhenskaya
and Ural’tseva to the settings of the Morrey spaces.},
	keywords = {Quasilinear elliptic equation; Weak solution; Hölder continuity; Morrey space},
	pages = {153--157}
}
@article{
	11589_10583,
	author = { PALAGACHEV D.K.},
	title = {Gary M. Lieberman: "Oblique Derivative Problems for Elliptic Equations"},
	year = {2014},
	journal = {JAHRESBERICHT DER DEUTSCHEN MATHEMATIKER-VEREINIGUNG},
	volume = {116},
	url = {http://link.springer.com/article/10.1365/s13291-013-0072-4},
	doi = {10.1365/s13291-013-0072-4},	
	pages = {79--84}
}
@article{
	11589_1057,
	author = { BYUN S -S  and  PALAGACHEV D K  and  RYU S },
	title = {Elliptic obstacle problems with measurable coefficients in non-smooth domains},
	year = {2014},
	journal = {NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION},
	volume = {35},
	abstract = {We establish a global weighted $W^{1,p}$-regularity for solutions to variational inequalities and obstacle problems
for divergence form elliptic systems with measurable coefficients in bounded non-smooth domains.},
	keywords = {Elliptic obstacle problem; Global weighted $L^p$-estimates; Measurable coefficients; small BMO; Reifenberg flat domain},
	url = {http://www.tandfonline.com/doi/abs/10.1080/01630563.2014.895753},
	doi = {10.1080/01630563.2014.895753},	
	pages = {893--910}
}
@conference{
	11589_16515,
	author = { DI LECCE  V  and  Casale  A  and  Soldo  D  and  Palagachev  D K  and  Uricchio  V },
	title = {Remote sensing organic matter identification in Apulia Region SoS-Soil project},
	year = {2014},
	publisher = {IEEE},
	address = {Piscataway (NJ)},
	booktitle = {INISTA 2014 - Innovations in Intelligent Systems and Applications, 2014 IEEE International Symposium},
	abstract = {Advances in remote sensing technology are now providing tools to support geospatial mapping of the soil properties for the application to the management of agriculture and the environment. In this paper results of visible and near IR spectral reflectance are presented and discussed. A supportable evaluation of organic matter in the soil is the absence of a specific signature, this concept arose out of the widely shared observation of scientific community in this concern. The obtained results show that a morphologic approach based on an experimental distance model is an appropriate and efficient method to deal with this matter},
	keywords = {organic matter; remote sensing; reflectance spectroscopy},
	url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6873651},
	doi = {10.1109/INISTA.2014.6873651},	
	pages = {398--405}
}
@article{
	11589_7439,
	author = { BYUN S -S  and  PALAGACHEV D K },
	title = {Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains},
	year = {2014},
	journal = {CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS},
	volume = {49},
	abstract = {We derive global gradient estimates in Morrey spaces for the weak solutions to discontinuous quasilinear elliptic equations related to important variational problems arising in models of 
linearly elastic laminates and composite materials.
 The principal coefficients of the quasilinear operator are supposed to be merely measurable in one variable and to have small-BMO seminorms in the remaining orthogonal directions, and the nonlinear terms are subject to controlled growth conditions with respect to the unknown function and its gradient. The boundary of the domain considered is Reifenberg flat which includes boundaries with rough fractal structure.  As outgrowth of the main result we get global Hoelder continuity of the weak solution with exact value of the corresponding exponent.},
	keywords = {Measurable coefficients; Reifenberg flat domain; Morrey space; Hoelder continuity; Linear laminates},
	url = {http://link.springer.com/article/10.1007%2Fs00526-012-0574-4},
	doi = {10.1007/s00526-012-0574-4},	
	pages = {37--76}
}
@article{
	11589_6658,
	author = { BYUN S -S  and  PALAGACHEV D K },
	title = {Weighted L^p-estimates for elliptic equations with measurable coefficients in nonsmooth domains},
	year = {2014},
	journal = {POTENTIAL ANALYSIS},
	volume = {41},
	abstract = {We obtain a global weighted $L^p$ estimate for the gradient of the weak solutions to
divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one variable and to have small BMO semi-norms in the remaining variables, while the boundary of the domain is supposed to be Reifenberg flat, which goes beyond the category of domains with Lipschitz continuous boundaries. As consequence of the main result, we derive global gradient estimate for the weak solution in the framework of the Morrey spaces which implies global  H\"older continuity of the solution.},
	keywords = {Elliptic equation; Measurable coefficients; Gradient estimates; Muckenhoupt weight; Weighted L^p space; Reifenberg flat domain},
	url = {http://link.springer.com/article/10.1007%2Fs11118-013-9363-8},
	doi = {10.1007/s11118-013-9363-8},	
	pages = {51--79}
}
@conference{
	11589_60293,
	author = { Bartolo  Rossella  and  Capozzi  Alberto  and  Cerami  Giovanna  and  Cingolani  Silvia  and  D’Avenia  Pietro  and  Greco  Carlo  and  Palagachev  Dian  and  Pomponio  Alessio  and  Vannella  Giuseppina },
	title = {Variational methods in the study of nonlinear problems and applications},
	year = {2014},
	publisher = {Gangemi Editore spa},
	address = {Roma},
	volume = {B},
	booktitle = {I gruppi di ricerca sfide tecnologiche e sociali},
	abstract = {In this paper we illustrate the lineguides of our research group. We describe some 
recent results concerning the study of some nonlinear differential equations and systems 
having a variational nature and arising from physics, geometry and applied sciences. In 
particular we report existence, multiplicity and regularity results for the solutions of these 
nonlinear problems. We point out that, in treating the above problems, the used methods for 
finding solutions are variational and topological, indeed the existence of solutions of the 
considered equations is obtained searching for critical points of suitable functionals defined on 
manifolds embedded into infinite dimensional functional spaces, while the regularity of the 
solutions is studied by means of geometric and harmonic analysis tools.},
	keywords = {Nonlinear Partial Differential Equations, Solutions, Existence, Multiplicity, Regularity},
	pages = {179--183}
}
@article{
	11589_2677,
	author = { BYUN S -S  and  PALAGACHEV D K  and  RYU S },
	title = {Weighted W^{1,p} estimates for solutions of nonlinear parabolic equations},
	year = {2013},
	journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY},
	volume = {45},
	abstract = {We are concerned with optimal regularity theory in weighted Sobolev spaces for discontinuous nonlinear parabolic problems in divergence form over a non-smooth bounded domain. 
Assuming smallness in BMO of the principal part of the nonlinear operator and flatness in Reifenberg sense of the boundary we establish a global weighted $W^{1,p}$ 
estimate for the weak solutions of such problems by
proving that the spatial gradient and the nonhomogeneous term
belong to the same weighted Lebesgue space.
The result is new in the settings of nonlinear parabolic problems.},
	url = {http://blms.oxfordjournals.org/content/early/2013/03/11/blms.bdt011},
	doi = {10.1112/blms/bdt011},	
	pages = {765--778}
}
@article{
	11589_7343,
	author = { BYUN S -S  and  PALAGACHEV D K },
	title = {Quasilinear elliptic equations with Morrey data},
	year = {2013},
	journal = {COMPTES RENDUS DE L'ACADÉMIE BULGARE DES SCIENCES},
	volume = {66},
	abstract = {We obtain global essential boundedness and H\"older continuity of the weak solutions  to quasilinear elliptic equations in divergence form with data lying in Morrey spaces.},
	keywords = {Quasilinear elliptic operator; Discontinuous coefficients; Morrey space; Essential boundedness; H\"older continuity},
	pages = {5--12}
}
@article{
	11589_7578,
	author = { BYUN S -S  and  PALAGACHEV D K },
	title = {Boundedness of the weak solutions to quasilinear  elliptic equations with Morrey data},
	year = {2013},
	journal = {INDIANA UNIVERSITY MATHEMATICS JOURNAL},
	volume = {62},
	abstract = {We prove global essential boundedness of weak solutions to quasilinear coercive divergence form equations with data belonging to Morrey spaces. The nonlinear terms are given in terms of Carath\'eodory functions and satisfy controlled growth assumptions.  As an application of the main result, we get global H\"older continuity of the solutions to semilinear elliptic equations with measurable coefficients and Morrey data.},
	keywords = {Quasilinear elliptic operator; Discontinuous coeffcients; Morrey space; Essential boundedness,; Hoelder continuity},
	url = {http://www.iumj.indiana.edu/IUMJ/Preprints/5115.pdf},
	doi = {10.1512/iumj.2013.62.5115},	
	pages = {1565--1585}
}
@article{
	11589_9874,
	author = { BYUN S -S  and  PALAGACHEV D K  and  WANG L },
	title = {Parabolic systems with measurable coefficients in Reifenberg domain},
	year = {2013},
	journal = {INTERNATIONAL MATHEMATICS RESEARCH NOTICES},
	volume = {2013},
	abstract = {We consider a parabolic system in divergence form with measurable coefficients in a nonsmooth bounded domain to obtain a global gradient estimate for the weak solution in the setting of Orlicz space which is a natural generalization of Lp space. The coefficients are assumed to be merely measurable in one spatial variable and have small bounded mean oscillation semi-norms in all the other variables. The boundary of the domain can be locally approximated by a hyperplane, a so-called δ-Reifenberg domain which is beyond the Lipschitz category.},
	keywords = {Gradient estimates, Orlicz space, Parabolic system, Measurable coefficients, Reifenberg domains},
	url = {http://imrn.oxfordjournals.org/content/early/2012/05/31/imrn.rns142},
	doi = {10.1093/imrn/rns142},	
	pages = {3053--3086}
}
@conference{
	11589_18670,
	author = { L  Riccardi  and  Naso D  and  B  Turchiano  and  H  Janocha  and  D  K  Palagachev },
	title = {On PID control of dynamic systems with hysteresis using a Prandtl-Ishlinskii model},
	year = {2012},
	publisher = {2012 American Control Conference},
	address = {Montreal, Canada},
	booktitle = {Proceedings of American Control Conference, June 2012, Montreal, Canada},
	abstract = {This papers deals with PI and PID control of second order systems with an input hysteresis described by a modified Prandtl-Ishlinskii model. The problem of the asymptotic tracking of constant references is re-formulated as the stability of a polytopic linear differential inclusion. This offers a simple linear matrix inequality condition that, when satisfied with the chosen PI or PID controller gains, ensures the tracking of constant reference and also allows the design to establish a performance index. The validation of the approach is performed experimentally on a Magnetic Shape Memory Alloy micrometric positioning system},
	keywords = {PID control; Mechatronics},
	url = {http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6315107&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F6297579%2F6314593%2F06315107.pdf%3Farnumber%3D6315107},
	doi = {10.1109/ACC.2012.6315107},	
	pages = {1670--1675}
}
@article{
	11589_6326,
	author = { PALAGACHEV D K  and  SOFTOVA L G },
	title = {Quasilinear divergence form parabolic equations in Reifenberg flat domains},
	year = {2011},
	journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS},
	volume = {31},
	abstract = {We derive weak solvability and higher integrability of the spatial gradient of solutions to Cauchy-Dirichlet problem for divergence form quasi-linear parabolic equations

{u(t) - div (a(ij)(x, t, u)D(j)u + a(i)(x, t, u)) = b(x, t, u, Du) in Q,

u = 0 on partial derivative(p)Q,

where Q is a cylinder in R(n) x (0, T) with Reifenberg flat base Omega. The principal coefficients a(ij)(x, t, u) of the uniformly parabolic operator are supposed to have small BMO norms with respect to (x, t) while the nonlinear terms a(i)(x, t, u) and b(x, t, u, Du) support controlled growth conditions.},
	keywords = {Divergence form quasilinear parabolic equations; Weak solvability; Discontinuous coefficients; Reifenberg flat domain; Small BMO; Controlled growth},
	url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=6518},
	doi = {10.3934/dcds.2011.31.1397},	
	pages = {1397--1410}
}
@article{
	11589_8828,
	author = { PALAGACHEV D K  and  SOFTOVA L G },
	title = {The Calderón–Zygmund property for quasilinear divergence form equations over Reifenberg flat domains},
	year = {2011},
	journal = {NONLINEAR ANALYSIS},
	volume = {74},
	abstract = {The results by Palagachev (2009) [3] regarding global Holder continuity for the weak solutions to quasilinear divergence form elliptic equations are generalized to the case of nonlinear terms with optimal growths with respect to the unknown function and its gradient. Moreover, the principal coefficients are discontinuous with discontinuity measured in terms of small BMO norms and the underlying domain is supposed to have fractal boundary satisfying a condition of Reifenberg flatness. The results are extended to the case of parabolic operators as well.},
	keywords = {Divergence form quasilinear elliptic and parabolic equations; Weak solutions; Hoelder continuity; Reifenberg domain; BMO},
	url = {http://www.sciencedirect.com/science/article/pii/S0362546X10007601},
	doi = {10.1016/j.na.2010.10.044},	
	pages = {1721--1730}
}
@article{
	11589_9686,
	author = { PALAGACHEV D.K.},
	title = {Quasilinear divergence form elliptic equations in rough domains},
	year = {2010},
	journal = {COMPLEX VARIABLES AND ELLIPTIC EQUATIONS},
	volume = {55},
	abstract = {Existence and global Holder continuity are proved for the weak solution to the Dirichlet problem

{div(a(ij)(x, u)D(j)u + a(t)(x, u)) = b(x, u, Du) in Omega subset of R(n),

u = 0 on partial derivative Omega

over Reifenberg flat domains Omega. The principal coefficients a(ij)(x, u) are discontinuous with respect to x with small BMO-norms and b(x, u, Du) grows as vertical bar Du vertical bar(r) with r < 1 + 2/n.},
	keywords = {divergence form quasilinear elliptic equations, weak solvability, Holder regularity, a priori estimates, Reifenberg flat domain, BMO},
	url = {http://www.tandfonline.com/doi/abs/10.1080/17476930903276159},
	doi = {10.1080/17476930903276159},	
	pages = {581--591}
}