@conference{
	11589_20518,
	author = { Caponio E  and  Devillanova G  and  Maddalena F  and  Masiello A  and  Solimini S },
	title = {Problems in Calculus of Variations and Nonlinear Analysis},
	year = {2014},
	publisher = {Cangemi Editore},
	booktitle = {Proceedings of the ``1st Workshop on the State of the Art and Challenges of Research Efforts at POLIBA,  03--05 dicembre 2014, Bari, Italy},
	pages = {227--331}
}
@article{
	11589_6752,
	author = { Granieri  and  L  and  Maddalena F },
	title = {A Metric Approach to Elastic Reformations},
	year = {2014},
	journal = {ACTA APPLICANDAE MATHEMATICAE},
	volume = {133},
	abstract = {We study a variational framework to compare shapes, modeled as Radon measures on ℝN, in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as integral functionals having some kind of isometries as minimizers. The approach pursued is based on the notion of pointwise Lipschitz constant leading to a matric space framework. In particular, to compare general shapes, we study this reformation problem by using the notion of transport plan and Wasserstein distances as in optimal mass transportation theory.},
	keywords = {Elasticity; Calculus of variations; Geometric measure theory},
	doi = {10.1007/s10440-013-9862-z},	
	pages = {153--185}
}
@article{
	11589_52325,
	author = { Florio G  and  Devillanova G  and  Maddalena F },
	title = {Blow-up of the quantum potential
for a free particle in one dimension},
	year = {2013},
	journal = {IL NUOVO CIMENTO C},
	volume = {36},
	abstract = {We derive a non-linear differential equation that must be satisfied by
the quantum potential, in the context of the Madelung equations, in one dimension
for a particular class of wave functions. In this case, we exhibit explicit conditions
leading to the blow-up of the quantum potential of a free particle at the boundary
of the compact support of the probability density.},
	keywords = {Quantum mechanics, Formalism, Ordinary differential equations},
	pages = {83--93}
}
@article{
	11589_52193,
	author = { Maddalena F  and  Solimini S },
	title = {Synchronic and asynchronic descriptions of irrigation problems.},
	year = {2013},
	journal = {ADVANCED NONLINEAR STUDIES},
	volume = {13},
	abstract = {In this paper we complete our work started in [31], where the present paper was announced;
in order to set a unified theory of the irrigation problem. The main result of the paper is the
equivalence of the various formulations introduced so far as well as a new one introduced
here. To this aim we introduce several geometric and analytical concepts which are essential
for reaching our final goal even if they may deserve an intrinsic interest in themselves.},
	keywords = {Irrigation problems; branched transportation networks; optimal mass transportation.},
	pages = {583--623}
}
@inbook{
	11589_11824,
	author = { MADDALENA F  and  PERCIVALE D  and  TOMARELLI F },
	title = {Elastic structures in adhesion interaction},
	year = {2012},
	publisher = {Springer},
	journal = {SPRINGER OPTIMIZATION AND ITS APPLICATIONS},
	volume = {66},
	booktitle = {Variational Analysis and Aerospace Engineering II},
	pages = {289--304}
}
@article{
	11589_3836,
	author = { Granieri  and  L  and  Maddalena F },
	title = {Transport Problems and Disintegration
Maps},
	year = {2012},
	journal = {ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS},
	volume = {19},
	abstract = {By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.},
	keywords = {Calculus of variations; Geometric measure theory; Optimal mass transportation theory},
	url = {http://dx.doi.org/10.1051/cocv/2012037},
	doi = {10.1051/cocv/2012037},	
	pages = {888--905}
}
@article{
	11589_9954,
	author = { FOSDICK R  and  GRANIERI L  and  MADDALENA F },
	title = {Reformation instability in elastic solids},
	year = {2012},
	journal = {JOURNAL OF ELASTICITY},
	volume = {107},
	abstract = {The reformation of a body fundamentally involves the mapping of one natural reference configuration of it into another natural reference configuration. The mass and the constitutive properties of the material remain unaltered, but the overall shape of the reference configuration generally changes. If, when a natural reference configuration is distorted, there is a portion of the boundary of the body that is displacement controlled, then a reformation of the body must be such that the original displacement controlled part of the boundary and its reformation are identical. In common applications that involve reformation, the remainder of the boundary is traction-free and a reformation essentially involves a change of the morphology of this traction-free surface. For example, undulations are often a characteristic feature of the reformation of a free, plane boundary surface. Reformations are a result of a material instability and they may associate with a chemically induced diffusive processes in which particles of the body move into preferred places. Fundamentally, a reformation is generated in response to the drive to lower the total stored energy of the body. In this work we are not concerned with the physical processes that take place during reformation, but rather we are concerned with characterizing the onset of the instability. We develop a variational characterization of the reformation instability for a nonlinear elastic body and we include the effect of surface energy. As an example, we consider the axial deformation of a circular cylinder and argue that small scale nano-wires, for which the diameter-to-length ratio is sufficiently small, are expected to be stable with respect to spatial variations when extended. Moreover, we observe that if the surfacial energy function is sufficiently convex at the undistorted state such wires may also be stable with respect to spatial variations when compressed. We then show that such small scale nano-wires are unstable with respect to reformation when either extended or compressed. © 2011 Springer Science+Business Media B.V.},
	keywords = {Instability; Nonlinear elasticity; Reformation},
	url = {http://link.springer.com/article/10.1007%2Fs10659-011-9348-z#/page-1},
	doi = {10.1007/s10659-011-9348-z},	
	pages = {131--150}
}
@article{
	11589_6412,
	author = { MADDALENA F  and  PERCIVALE D  and  TOMARELLI F },
	title = {Adhesive flexible material structures},
	year = {2012},
	journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.},
	volume = {17},
	abstract = {We study variational problems modeling the adhesion interaction with a rigid substrate for elastic strings and rods. We produce conditions characterizing bonded and detached states as well as optimality properties with respect to loading and geometry. We show Euler equations for minimizers of the total energy outside self-contact and secondary contact points with the substrate.},
	keywords = {Adhesion; Calculus of variations; Nonlinear elasticity},
	url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=6835},
	doi = {10.3934/dcdsb.2012.17.553},	
	pages = {553--574}
}
@article{
	11589_9958,
	author = { DASSISTI M  and  MADDALENA F  and  BRANCOLINI A  and  CHIMENTI M  and  GRANIERI L },
	title = {Variational techniques for assessing the technological signature of flat surfaces},
	year = {2011},
	journal = {OPTIMIZATION AND ENGINEERING},
	volume = {14},
	abstract = {The quality assessment of manufacturing operations performed to obtain given flat surfaces is always a problem of comparing the substitute model (approximating the features of the true manufactured part) to the nominal specifications, at any stage of the manufacturing cycle. A novel methodology, based on applications of classical tools of Calculus of Variations, is here presented with the aim of assessing the output quality of manufactured flat surfaces based on the information available on transformation imposed by technological processes. By assuming that any manufacturing process operates under equilibrium states, the proposed variational methodology allows to account for the traces left by different stages of manufacturing processes. A simple two-dimensional case is here discussed, to give the flavor of the methodology and its future potential developments.},
	keywords = {Calculus of variation; Flat surfaces; Quality assessment},
	url = {http://link.springer.com/content/pdf/10.1007%252Fs11081-011-9173-z.pdf},
	doi = {10.1007/s11081-011-9173-z},	
	pages = {155--174}
}
@article{
	11589_1947,
	author = { Maddalena F  and  Percivale D  and  Puglisi G },
	title = {Energy minimizing states in adhesion problems for elastic rods},
	year = {2010},
	journal = {APPLIED MATHEMATICAL SCIENCES},
	volume = {4},
	abstract = {In this paper we analyze and compare two different models for adhesion
phenomena, recently proposed by the authors. In the first approach
[9] a feasible expression of the adhesion energy is suggested by the existence
problem of partially detached equilibrium states. In the second
model [10] the macroscopic energy is obtained by performing a multiscale
analysis and it is deduced via a macroscopic Γ-limit of the energy
at the scale of the microstructure. Interestingly, we obtain that the first
model can be deduced by the second one as the limit case when the
parameter measuring the relative stiffness of the adhesive layer and the
beam diverges.},
	pages = {3749--3760}
}
@article{
	11589_2253,
	author = { Granieri  L  and  Maddalena  F },
	title = {On some variational problems involving volume and surface energies},
	year = {2010},
	journal = {JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS},
	volume = {146},
	abstract = {We show how some problems coming from different fields of applied sciences, such as physics, engineering, biology, admit a common variational formulation characterized by the competition of two energetic terms. We discuss related problems and techniques studied by the authors and collaborators in the recent past as well open problems and further possible research directions in these topics.},
	keywords = {Applied variational methods; Calculus of variations; Shape optimization},
	doi = {10.1007/s10957-010-9660-y},	
	pages = {359--374}
}
@article{
	11589_9267,
	author = { MADDALENA F  and  SOLIMINI S },
	title = {Transport distances and irrigation models},
	year = {2009},
	journal = {JOURNAL OF CONVEX ANALYSIS},
	volume = {16},
	pages = {121--152}
}
@article{
	11589_2173,
	author = { P  D'AMBROSIO  and  DE TOMMASI D  and  L  GRANIERI  and  F  MADDALENA },
	title = {A surface energy approach to the mass reduction
problem for elastic bodies},
	year = {2009},
	journal = {IMA JOURNAL OF APPLIED MATHEMATICS},
	volume = {74},
	doi = {10.1093/imamat/hxp031},	
	pages = {934--949}
}
@article{
	11589_2178,
	author = { Maddalena F  and  Percivale D  and  Puglisi G  and  Truskinovsky L },
	title = {Mechanics of reversible unzipping},
	year = {2009},
	journal = {CONTINUUM MECHANICS AND THERMODYNAMICS},
	volume = {21},
	abstract = {We study the mechanics of a reversible decohesion (unzipping) of an elastic layer subjected to
quasi-static end-point loading. At the micro level the system is simulated by an elastic chain of particles interacting
with a rigid foundation through breakable springs. Such system can be viewed as prototypical for the
description of a wide range of phenomena from peeling of polymeric tapes, to rolling of cells, working of
Gecko’s fibrillar structures and denaturation of DNA. We construct a rigorous continuum limit of the discrete
model which captures both stable and metastable configurations and present a detailed parametric study of the
interplay between elastic and cohesive interactions. We show that the model reproduces the experimentally
observed abrupt transition from an incremental evolution of the adhesion front to a sudden complete decohesion
of a macroscopic segment of the adhesion layer. As the microscopic parameters vary the macroscopic
response changes from quasi-ductile to quasi-brittle, with corresponding decrease in the size of the adhesion
hysteresis. At the micro-scale this corresponds to a transition from a ‘localized’ to a ‘diffuse’ structure of the
decohesion front (domain wall). We obtain an explicit expression for the critical debonding threshold in the
limit when the internal length scales are much smaller than the size of the system. The achieved parametric
control of the microscopic mechanism can be used in the design of new biological inspired adhesion devices
and machines.},
	keywords = {Unzipping; Adhesion; Peeling; Hysteresis; DNA; Gecko; Calculus of variations},
	doi = {10.1007/s00161-009-0108-2},	
	pages = {251--268}
}
@article{
	11589_9677,
	author = { MADDALENA F  and  PERCIVALE D },
	title = {Variational models for peeling problems},
	year = {2008},
	journal = {INTERFACES AND FREE BOUNDARIES},
	volume = {10},
	pages = {503--516}
}