Sobolev estimates for non-uniformly parabolic PDEs

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Abstract

Sobolev energy estimates are proven for solutions of initial-value-problems for non-uniformly parabolic second-order PDEs having symmetric coefficients depending on the independent and dependent variables. Local-in-time existence of solutions to initial-value problems for such systems and convergence results for singular limits involving such systems are consequences of those uniform bounds.

Original languageEnglish
Article number13
JournalPartial Differential Equations and Applications
Volume3
Issue number1
DOIs
StatePublished - Feb 2022

Keywords

  • Non-uniformly parabolic
  • Sobolev energy estimates
  • singular limit

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