Sobolev estimates for non-uniformly parabolic PDEs

Steve Schochet ()
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Steve Schochet: Tel Aviv University

Partial Differential Equations and Applications, 2022, vol. 3, issue 1, 1-25

Abstract: 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.

Keywords: Non-uniformly parabolic; Sobolev energy estimates; singular limit; 35K65; 35K45; 35B45; 35B25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00149-4

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