Graphs of finite mass which cannot be approximated in area by smooth graphs

DOI10.1007/BF02599312zbMath0796.58006OpenAlexW2060089518MaRDI QIDQ1313526

Giuseppe Modica, Mariano Giaquinta, Jiří Souček

Publication date: 22 September 1994

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155807

zbMATH Keywords

approximationcurrentsgraphs

Mathematics Subject Classification ID

Vector-valued measures and integration (46G10) Set-valued and function-space-valued mappings on manifolds (58C06)

Related Items

New lower semicontinuity results for polyconvex integrals, Currents carried by the graphs of semi-monotone maps, Strict convergence with equibounded area and minimal completely vertical liftings, Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measures, Connectivity properties of the range of a weak diffeomorphism, Approximation in area of graphs with isolated singularities, Graphs of finite mass which cannot be approximated by smooth graphs with equibounded area, Area and the area formula, Relaxed area of graphs of piecewise Lipschitz maps in the strict \(BV\)-convergence, Approximation in Sobolev spaces of nonlinear expressions involving the gradient, On the total variation of the Jacobian., Approximation in area of continuous graphs, Weak notions of Jacobian determinant and relaxation, Approximation problems for curvature varifolds

Cites Work

• Infima of energy functionals in homotopy classes of mappings
• Homotopy classes in Sobolev spaces and the existence of energy minimizing maps
• Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity
• The approximation problem for Sobolev maps between two manifolds
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