Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity

Stanislav Antontsev, Sergey Shmarev

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We consider the homogeneous Dirichlet problem for the equation [Formula presented], d≥2, with the variable exponent [Formula presented], p±=const. We find sufficient conditions on p, ∂Ω, f and u(x,0) which provide the existence of solutions with the following global regularity properties: [Formula presented] For the solutions of the stationary counterpart of Eq. (0.1), [Formula presented] on ∂Ω,the inclusions [Formula presented] are established.

Original languageEnglish
Article number111724
Number of pages29
JournalNonlinear Analysis, Theory, Methods and Applications
Volume195
DOIs
Publication statusPublished - Jun 2020

Keywords

  • Higher regularity
  • Singular parabolic equation
  • Strong solutions
  • Variable nonlinearity
  • P(X
  • CONTINUITY
  • SYSTEMS
  • HIGHER REGULARITY

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