We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.
|Number of pages||14|
|Journal||Archive for Rational Mechanics and Analysis|
|Publication status||Published - 2008|
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering