We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In case of Poisson equation, our proof is alternative to the ones proposed by Serrin (moving planes) and by Weinberger, and it makes no direct use of the maximum principle, while it enlightens a relation between Serrin problem and isoperimetric inequality.
Serrin type overdetermined problems: an alternative proof / Brandolini, Barbara; Nitsch, Carlo; P., Salani; Trombetti, Cristina. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 190:2(2008), pp. 267-280. [10.1007/s00205-008-0119-3]
Serrin type overdetermined problems: an alternative proof
BRANDOLINI, BARBARA;NITSCH, CARLO;TROMBETTI, CRISTINA
2008
Abstract
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In case of Poisson equation, our proof is alternative to the ones proposed by Serrin (moving planes) and by Weinberger, and it makes no direct use of the maximum principle, while it enlightens a relation between Serrin problem and isoperimetric inequality.| File | Dimensione | Formato | |
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