Improvement of flatness for vector valued free boundary problems
| Autor: | Giorgio Tortone, Daniela De Silva |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
viscosity solution
Scalar problem lcsh:T57-57.97 Applied Mathematics harnack inequality 010102 general mathematics Scalar (mathematics) Mathematical analysis 01 natural sciences improvement of flatness 010101 applied mathematics Mathematics - Analysis of PDEs lcsh:Applied mathematics. Quantitative methods Free boundary problem FOS: Mathematics vectorial problem 0101 mathematics Fractional Laplacian Viscosity solution one-phase free boundary problem Mathematical Physics Analysis Mathematics Harnack's inequality Analysis of PDEs (math.AP) |
| Zdroj: | Mathematics in Engineering, Vol 2, Iss 4, Pp 598-613 (2020) |
| DOI: | 10.48550/arxiv.1909.01290 |
| Popis: | For a vectorial Bernoulli-type free boundary problem, with no sign assumption on the components, we prove that flatness of the free boundary implies $C^{1,\alpha}$ regularity, as well-known in the scalar case \cite{AC,C2}. While in \cite{MTV2} the same result is obtained for minimizing solutions by using a reduction to the scalar problem, and the NTA structure of the regular part of the free boundary, our result uses directly a viscosity approach on the vectorial problem, in the spirit of \cite{D}. We plan to use the approach developed here in vectorial free boundary problems involving a fractional Laplacian, as those treated in the scalar case in \cite{DR, DSS}. Comment: 13 pages |
| Databáze: | OpenAIRE |
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