On the optimality of certain Sobolev exponents for the weak continuity of determinants

DOI10.1016/0022-1236(92)90071-PzbMath0769.46025OpenAlexW2040777666MaRDI QIDQ1187763

Bernard Dacorogna, François Murat

Publication date: 23 July 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90071-p

zbMATH Keywords

Radon measureoptimality of Sobolev exponentsweak continuity of determinant

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (12)

A new div-curl result. applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian ⋮ Polyharmonic \(k\)-Hessian equations in \(\mathbb{R}^N\) ⋮ The distributional hyper-Jacobian determinants in fractional Sobolev spaces ⋮ A brief history of the Jacobian ⋮ The Jacobian determinant revisited ⋮ On the distributional Jacobian of maps from \(\mathbb{S}^N\) into \(\mathbb{S}^N\) in fractional Sobolev and Hölder spaces ⋮ Estimates for the topological degree and related topics ⋮ On polyharmonic regularizations of \(k\)-Hessian equations: variational methods ⋮ On the integrability of the Jacobian under minimal hypotheses ⋮ The div-curl lemma ``trente ans après: an extension and an application to the \(G\)-convergence of unbounded monotone operators ⋮ Weak continuity and lower semicontinuity results for determinants ⋮ Optimal function spaces for continuity of the Hessian determinant as a distribution

Cites Work

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• \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• Semicontinuity and relaxation for integrals depending on vector valued functions
• Convexity conditions and existence theorems in nonlinear elasticity
• Stability theorems for mappings with bounded excursions
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• Direct methods in the calculus of variations

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