### Analysis and Probability SeminarOn a Bernoulli-Type Overdetermined Free Boundary ProblemMariana Smit Vega Garcia (Western Washington University)

Friday, February 14, 2020
3:30pm – 4:30pm

Storrs Campus
MONT 214

Abstract: We study a Bernoulli-type free boundary problem in the context of A-harmonic PDEs. In particular, we show that if K is a bounded convex set satisfying the interior ball condition and $$c>0$$ is a given constant, then there exists a unique convex domain U containing K and a function u which is A-harmonic in $$U\setminus K$$, has continuous boundary values 1 on $$\partial K$$ and 0 on $$\partial U$$, such that $$|\nabla u| =c$$ on $$\partial U$$. Moreover, $$\partial U$$ is $$C^{1,\gamma}$$, for some $$\gamma>0$$, and it is smooth provided A is smooth in $$\mathbb{R}^n\setminus\{0\}$$.

Contact:

scott.zimmerman@uconn.edu

Analysis and Probability Seminar (primary), Analysis Learning Seminar, UConn Master Calendar