6533b7cffe1ef96bd12590c6

RESEARCH PRODUCT

Serrin-Type Overdetermined Problems: an Alternative Proof

Cristina TrombettiPaolo SalaniCarlo NitschBarbara Brandolini

subject

Hessian equationMechanical EngineeringMathematical analysisMathematics::Analysis of PDEsHessian equationType (model theory)isoperimetric inequalityMathematical proofOverdetermined systemNonlinear systemMathematics (miscellaneous)Maximum principleSettore MAT/05 - Analisi Matematicasymmetry of solutionsOverdetermined problemApplied mathematicsIsoperimetric inequalityPoisson's equationAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2008-08-12Archive for Rational Mechanics and Analysis
https://doi.org/10.1007/s00205-008-0119-3