• Corpus ID: 220525479

Duality arguments for linear elasticity problems with incompatible deformation fields

  title={Duality arguments for linear elasticity problems with incompatible deformation fields},
  author={Adriana Garroni and Annalisa Malusa},
  journal={arXiv: Analysis of PDEs},
We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence of the operators. In particular the homogenization procedure, valid for elliptic systems in linear elasticity, depicts the macroscopic features of a composite material in the presence of plastic deformation. 


Definition and existence of renormalized solutions of elliptic equations with general measure data
Abstract We introduce a new definition of solution for the nonlinear monotone elliptic problem-div(a(a;, ∇u)) = μ in Ω u = 0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω. We prove
Topics in the Mathematical Modelling of Composite Materials
On the control of partial differential equations estimation of homogenized coefficients H-convergence a strange term coming from nowhere design of composite plates of extremal rigidity calculus of
Two semilinear Dirichlet problems “almost” in duality
In this paper we study two semilinear Dirichlet problems; the linear parts (in some sense, in duality) are a problem with singular convection term and a problem with singular drift. The nonlinear
New estimates for elliptic equations and Hodge type systems
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension n, with data in L1. We also present related results concerning differential
The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations
We prove that the classical line-tension approximation for dislocations in crystals, that is, the approximation that neglects interactions at a distance between dislocation segments and accords
Homogenization of Differential Operators and Integral Functionals
1 Homogenization of Second Order Elliptic Operators with Periodic Coefficients.- 1.1 Preliminaries.- 1.2 Setting of the Homogenization Problem.- 1.3 Problems of Justification Further Examples.- 1.4
Existence and regularity results for relaxed Dirichlet problems with measure data
AbstractWe study the following relaxed Dirichlet problem $$\left\{ \begin{gathered} Lu + \mu u = vin\Omega , \hfill \\ u = 0on\partial \Omega , \hfill \\ \end{gathered} \right.$$ where Ω is a
On the nonexistence of Green's function and failure of the strong maximum principle
  • L. Orsina, A. Ponce
  • Physics, Mathematics
    Journal de Mathématiques Pures et Appliquées
  • 2020
Given any Borel function $V : \Omega \to [0, +\infty]$ on a smooth bounded domain $\Omega \subset \mathbb{R}^{N}$, we establish that the strong maximum principle for the Schr\"odinger operator
Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche
© Scuola Normale Superiore, Pisa, 1968, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze »
Sulla convergenza degli integrali dell''energia per operatori ellittici del secondo ordine
A foot for the sewing of blind stitches comprises a substantially vertically arranged shank portion having a lower end connected to a substantially flat foot sole which extends outwardly from the