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Local regularity for quasi-linear parabolic equations in non-divergence form

Amal Attouchi

subject

Applied Mathematics010102 general mathematicsMathematical analysisDegenerate energy levelsMathematics::Analysis of PDEsType (model theory)Lipschitz continuity01 natural sciencesParabolic partial differential equation010101 applied mathematicsViscosityMathematics - Analysis of PDEs35B65 35K65 35D40 35K92 35K6FOS: Mathematics0101 mathematicsDivergence (statistics)Laplace operatorAnalysisAnalysis of PDEs (math.AP)Flatness (mathematics)Mathematics

description

Abstract We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p -Laplacian type and in non-divergence form. We provide local Holder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Holder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.

yearjournalcountryeditionlanguage
2018-09-10Nonlinear Analysis
https://doi.org/10.1016/j.na.2020.112051