Serrin-type overdetermined problems: An alternative proof

Barbara Brandolini, Barbara Brandolini, Carlo Nitsch, Cristina Trombetti, Paolo Salani

Research output: Contribution to journalArticlepeer-review

54 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)267-280
Number of pages14
JournalArchive for Rational Mechanics and Analysis
Volume190
Publication statusPublished - 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this