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 S from D. Denote by |D| the volume of D and by |S| the area of S.
Theorem 1. Assume that the over-determined problem
is solvable. Then D is a ball.