Finite Distortion Sobolev Mappings between Manifolds are Continuous
| Autor: | Mohammad Reza Pakzad, Piotr Hajłasz, Paweł Goldstein |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Open set Boundary (topology) 30C65 (46E35 58C07) 01 natural sciences Omega Sobolev space Distortion (mathematics) symbols.namesake Mathematics - Classical Analysis and ODEs Jacobian matrix and determinant Classical Analysis and ODEs (math.CA) FOS: Mathematics symbols Almost everywhere 0101 mathematics Mathematics |
| Zdroj: | International Mathematics Research Notices. 2019:4370-4391 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnx251 |
| Popis: | We prove that if $M$ and $N$ are Riemannian, oriented $n$-dimensional manifolds without boundary and additionally $N$ is compact, then Sobolev mappings in $W^{1,n}(M,N)$ of finite distortion are continuous. In particular, $W^{1,n}(M,N)$ mappings with almost everywhere positive Jacobian are continuous. This result has been known since 1976 in the case of mappings in $W^{1,n}(\Omega,{\mathbb R}^n)$, where $\Omega\subset{\mathbb R}^n$ is an open set. The case of mappings between manifolds is much more difficult. |
| Databáze: | OpenAIRE |
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