A Comparison Theorem for Nonsmooth Nonlinear Operators

Vladimir Kozlov, Alexander Nazarov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity f is Lp function with p > 1. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given.

Original languageEnglish
Pages (from-to)471-481
Number of pages11
JournalPotential Analysis
Volume54
Issue number3
DOIs
StatePublished - Mar 2021

Scopus subject areas

  • Analysis

Keywords

  • Comparison principal
  • Kato classes
  • Non-smooth nonlinearity
  • Semi-linear elliptic equation
  • Strong maximum principle
  • VMO coefficients

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