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- Title
Sobolev homeomorphisms with gradients of low rank via laminates.
- Authors
Faraco, Daniel; Mora-Corral, Carlos; Oliva, Marcos
- Abstract
Let Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} be a bounded open set. Given 2 ≤ m ≤ n {2\leq m\leq n} , we construct a convex function u : Ω → ℝ {u\colon\Omega\to\mathbb{R}} whose gradient f = ∇ u {f=\nabla u} is a Hölder continuous homeomorphism, <italic>f</italic> is the identity on ∂ Ω {\partial\Omega} , the derivative <italic>Df</italic> has rank m - 1 {m-1} a.e. in Ω and <italic>Df</italic> is in the weak L m {L^{m}} space L m , w {L^{m,w}}. The proof is based on convex integration and staircase laminates.
- Subjects
SOBOLEV gradients; HOMEOMORPHISMS; CONVEX functions; MATHEMATICAL mappings; JACOBIAN determinants
- Publication
Advances in Calculus of Variations, 2018, Vol 11, Issue 2, p111
- ISSN
1864-8258
- Publication type
Article
- DOI
10.1515/acv-2016-0009