We prove the simmetry of solutions to overdetermined problems for Hessian equations, a class of fully nonlinear equations including Poisson equation and Monge-Ampère equation. 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 / B. BRANDOLINI; C. NITSCH; P. SALANI; C. TROMBETTI. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 190 n. 2:(2008), pp. 267-280. [10.1007/s00205-008-0119-3]
Serrin type overdetermined problems: an alternative proof
SALANI, PAOLO;
2008
Abstract
We prove the simmetry of solutions to overdetermined problems for Hessian equations, a class of fully nonlinear equations including Poisson equation and Monge-Ampère equation. 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 | |
|---|---|---|---|
|
BNSTArchRat.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
181.64 kB
Formato
Adobe PDF
|
181.64 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
