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.

Brandolini B., Nitsch C., Salani P., & Trombetti C. (2008). Serrin-type overdetermined problems: An alternative proof. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 190(2), 267-280 [10.1007/s00205-008-0119-3].

Serrin-type overdetermined problems: An alternative proof

Brandolini B.
;
2008

Abstract

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.
Settore MAT/05 - Analisi Matematica
Brandolini B., Nitsch C., Salani P., & Trombetti C. (2008). Serrin-type overdetermined problems: An alternative proof. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 190(2), 267-280 [10.1007/s00205-008-0119-3].
File in questo prodotto:
File Dimensione Formato  
ARMA(2008).pdf

non disponibili

Descrizione: articolo principale
Tipologia: Versione Editoriale
Dimensione 181.64 kB
Formato Adobe PDF
181.64 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/494032
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 58
  • ???jsp.display-item.citation.isi??? 60
social impact