Pathological Sobolev homeomorphisms in GFT and NE

Abstract: Sobolev homeomorphisms are the natural choice for minimization problems in non-linear elasticity. For the regularity of these problems it would be useful to be able to approximate these maps by smooth homeomorphisms in their corresponding Sobolev space (the so-called Ball-Evans problem). We construct a pair of homeomorphisms for which is impossible simultaneously solving the Hajlasz problem. That is we construct a Sobolev homeomorphism equalling identity on the boundary of a cube but with negative Jacobian almost everywhere.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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