Full regularity of the free boundary in a bernoulli-type problem in two dimensions

Donatella Danielli, Arshak Petrosyan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0} ∩Ω in the Bernoulli-type problem governed by the p-Laplace operator Jp(u) = ∫Ω (|∇u|P + λpp × {u>0}) dx → min, for p in the range 2 - ε0 < p < ∞ for an absolute constant ε0 > 0.

Original languageEnglish (US)
Pages (from-to)667-681
Number of pages15
JournalMathematical Research Letters
Volume13
Issue number4
DOIs
StatePublished - Jul 2006
Externally publishedYes

Keywords

  • Bernoulli-type problem
  • Free boundary problem
  • Full regularity
  • p-Laplacian

ASJC Scopus subject areas

  • Mathematics(all)

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