Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities

Paul M.N. Feehan, Camelia A. Pop

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We prove local supremum bounds, a Harnack inequality, Hölder continuity up to the boundary, and a strong maximum principle for solutions to a variational equation defined by an elliptic operator which becomes degenerate along a portion of the domain boundary and where no boundary condition is prescribed, regardless of the sign of the Fichera function. In addition, we prove Hölder continuity up to the boundary for solutions to variational inequalities defined by this boundary-degenerate elliptic operator.

Original languageEnglish (US)
Pages (from-to)1075-1129
Number of pages55
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume34
Issue number5
DOIs
StatePublished - May 29 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

Keywords

  • Degenerate diffusion process
  • Degenerate elliptic differential operator
  • Harnack inequality
  • Hölder continuity
  • Variational inequality
  • Weighted Sobolev space

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