Global higher regularity of solutions to singular p(x,t)-parabolic equations

Stanislav Antontsev, Ivan Kuznetsov, Sergey Shmarev

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We study the homogeneous Dirichlet problem for the equation ut=div(|∇u|p(x,t)−2∇u)+f(x,t,u) in the cylinder QT=Ω×(0,T), Ω⊂Rd, d≥2. It is assumed that p(x,t)∈([Formula presented],2) and |∇p|, |pt| are bounded a.e. in QT. We find conditions on p(x,t), f(x,t,u) and u(x,0) sufficient for the existence of strong solutions, local or global in time. It is proven that the strong solutions possess the property of global higher regularity: ut∈L2(QT), |∇u|∈L(0,T;L2(Ω)), |Dij 2u|p(x,t)∈L1(QT).

Original languageEnglish
Pages (from-to)238-263
Number of pages26
JournalJournal of Mathematical Analysis and Applications
Volume466
Issue number1
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • Higher regularity
  • Singular parabolic equation
  • Strong solutions
  • Variable nonlinearity
  • P-LAPLACIAN
  • CONTINUITY
  • PARABOLIC EQUATIONS

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