Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions

David Arcoya, Colette De Coster, Louis Jeanjean, Kazunaga Tanaka

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

In this note we present some uniqueness and comparison results for a class of problem of the form. (0.1)-Lu=H(x,u,∇;u)+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN, N≥. 2 is a bounded domain, L is a general elliptic second order linear operator with bounded coefficients and H is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp.

Original languageEnglish
Pages (from-to)772-780
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume420
Issue number1
DOIs
Publication statusPublished - 2014 Dec 1

Keywords

  • Quadratic growth in the gradient
  • Quasilinear elliptic equations
  • Uniqueness of solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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