Existence theorems for non convex problems

zbMath0522.49001MaRDI QIDQ1056046

Rosanna Schianchi, Elvira Mascolo

Publication date: 1983

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

non convex problemsmultiple integralsexistence of minima

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Related Items (17)

An anti-plane shear problem ⋮ An approach of deterministic control problems with unbounded data ⋮ Minimizing a functional depending on \(\nabla u\) and on \(u\) ⋮ Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals ⋮ A uniqueness result for a class of non-strictly convex variational problems ⋮ Existence of minimizers for non-quasiconvex integrals ⋮ Equilibrium configurations of crystals ⋮ General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases ⋮ Teoremi di esistenza del minimo per funzionali non convessi del calcolo delle variazioni ⋮ Analysis of microstructures and phase transition phenomena in one-dimensional, non-linear elasticity by convex optimization ⋮ Régularité de la solution d'un problème variationnel. (Regularity of the solution of a variational problem) ⋮ Parabolic equations and the bounded slope condition ⋮ Local minima of nonconvex problems ⋮ An existence result for a nonconvex variational problem via regularity ⋮ Calculus of variations, implicit partial differential equations and microstructure ⋮ Geometric constraints on the domain for a class of minimum problems ⋮ Sur une équation quasilinéaire d'ordre 2 non elliptique. (On a quasilinear nonelliptic equation of second order)

Cites Work

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• On the regularity of the minima of variational integrals
• Regolarita Lipschitziana per la soluzione di alcuni problemi di minimo con vincolo
• On some non-linear elliptic differential functional equations
• Linear and quasilinear elliptic equations
• Théorémes d'existence en optimisation non convexe
• Viscosity Solutions of Hamilton-Jacobi Equations
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
• Semicontinuity problems in the calculus of variations

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