Model problems from nonlinear elasticity:  
partial regularity results

Menita Carozza; Antonia Passarelli di Napoli

Displaying similar documents to “Model problems from nonlinear elasticity: partial regularity results”

On the Lower Semicontinuity of Supremal Functionals

Michele Gori, Francesco Maggi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study the lower semicontinuity problem for a supremal functional of the form $F (u, Ω) = \underset{x \in Ω}{ess \sup} f (x, u (x), D u (x))$ with respect to the strong convergence in (Ω), furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur's lemma for gradients of uniformly converging sequences is proved.

Geometric constraints on the domain for a class of minimum problems

Graziano Crasta, Annalisa Malusa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider minimization problems of the form $\min_{u \in ϕ + W_{0}^{1, 1} (Ω)} \int_{Ω} [f (D u (x)) - u (x)] d x$ where $Ω \subseteq ℝ^{N}$ is a bounded convex open set, and the Borel function $f : ℝ^{N} \to [0, + \infty]$ is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of and the zero level set of , we prove that the viscosity solution of a related Hamilton–Jacobi equation provides a minimizer for the integral functional.

The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We establish two new formulations of the membrane problem by working in the space of $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -Young measures and $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...