Beltrami equations in the plane and Sobolev regularity
| Autor: | Martí Prats |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Pure mathematics Conjecture Smoothness (probability theory) Plane (geometry) Applied Mathematics 010102 general mathematics Mathematics::Analysis of PDEs General Medicine 01 natural sciences Beltrami equation Fractional calculus 35J46 30C62 46E35 010101 applied mathematics Sobolev space Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Communications on Pure & Applied Analysis. 17:319-332 |
| ISSN: | 1553-5258 |
| DOI: | 10.3934/cpaa.2018018 |
| Popis: | New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\bar{\partial} f = \mu \partial f + \nu \overline{\partial f}$ for discontinuous Beltrami coefficients $\mu$ and $\nu$ are obtained, using Kato-Ponce commutators, obtaining that $\overline \partial f$ belongs to a Sobolev space with the same smoothness as the coefficients but some loss in the integrability parameter. A conjecture on the cases where the limitations of the method do not work is raised. Comment: 13 pages, 12 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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