On the A-obstacle problem and the Hausdorff measure of its free boundary

S. Challal, A. Lyaghfouri, J. F. Rodrigues

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

In this paper, we prove existence and uniqueness of an entropy solution to the A-obstacle problem, for L 1-data. We also extend the Lewy-Stampacchia inequalities to the general framework of L 1-data and show convergence and stability results. We then prove that the free boundary has finite (N - 1)-Hausdorff measure, which completes previous works on this subject by Caffarelli for the Laplace operator and by Lee and Shahgholian for the p-Laplace operator when p > 2.

Original languageEnglish
Pages (from-to)113-165
Number of pages53
JournalAnnali di Matematica Pura ed Applicata
Volume191
Issue number1
DOIs
Publication statusPublished - Jan 2012
Externally publishedYes

Keywords

  • A-Laplace operator
  • Entropy solution
  • Free boundary
  • Hausdorff measure
  • Lewy-Stampacchia inequalities
  • Obstacle problem
  • Stability

ASJC Scopus subject areas

  • Applied Mathematics

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