THE NASH INEQUALITY IN GENERAL DOMAINS WITH APPLICATION TO THE LINEAR STOKES SYSTEM

Matania Ben-Artzi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The well-known Nash inequality is extended to functions satisfying a weak Dirichlet condition in a subset of ℝn. Two versions of the inequality are established, with constants independent of the domain. The inequality is applied to obtain an estimate for the sup-norm of a solution to the linearized Stokes system, independent of the velocity field.

Original languageEnglish
Pages (from-to)287-294
Number of pages8
JournalPure and Applied Functional Analysis
Volume5
Issue number2
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, Yokohama Publications. All rights reserved.

Keywords

  • blow-up
  • general domains
  • linearized Stokes system
  • Nash inequality
  • weak Dirichlet condition

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