Two Phase Free Boundary Problem for Poisson Kernels

Autor:	Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro, Zihui Zhao
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Mathematics - Analysis of PDEs Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs General Mathematics Classical Analysis and ODEs (math.CA) FOS: Mathematics Metric Geometry (math.MG) Analysis of PDEs (math.AP)
Popis:	We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, the oscillation of the logarithm of the interior and exterior Poisson kernels yields a great deal of geometric information about the domain. We use techniques from the classical calculus of variations, potential theory, quantitative geometric measure theory to accomplish this. One feature of this work, compared to Bortz-Hofmann PAMS 16 and Kenig-Toro Crelle 06, is that a priori we only require that the domains in question are connected. 48 pages. Final version including many suggestions by the referee(s). To appear in IUMJ
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6492d9059feeaccc83ebf69c72248333 http://arxiv.org/abs/1908.03033 Zobrazit plný text záznamu