The main result of this paper is that if a C2 function u on Ω⊂R3 is a solution of the system (1) Δu=f(u) and |∇u|=g(u), then the level surfaces of u must be pieces of concentric spheres, concentric cylinders, or parallel planes. The above system is an important and interesting one and, while apparently not familiar to most analysts. Previous results in the case R2 were proved by Talenti with a completely different proof.
An overdetermined system
PUCCI, Patrizia
1983
Abstract
The main result of this paper is that if a C2 function u on Ω⊂R3 is a solution of the system (1) Δu=f(u) and |∇u|=g(u), then the level surfaces of u must be pieces of concentric spheres, concentric cylinders, or parallel planes. The above system is an important and interesting one and, while apparently not familiar to most analysts. Previous results in the case R2 were proved by Talenti with a completely different proof.File in questo prodotto:
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