Some Symmetry Results for PDE

Ramm A. G.

Published on: 2021-12-09

Abstract

Let  be a bounded connected domain in  with a smooth boundary S, N  is the outer unit normal to S, K > 0  is a constant,  is the limiting value of the normal derivative of u on from D. Denote by |D| the volume of and by |S| the area of S.

Theorem 1. Assume that the over-determined problem

is solvable. Then D is a ball.

Keywords

MSC; 35B06; 35R30; 35J05.