Hölder regularity for degenerate parabolic double-phase equations

2024/04/29 by Kim, Wontae, Moring, Kristian, Särkiö, Lauri · 3 citations
#35D30 #35K65 #35K92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.19111

Abstract

We prove that bounded weak solutions to degenerate parabolic double-phase equations of p-Laplace type are locally Hölder continuous. The proof is based on phase analysis and methods for the p-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the p-Laplace or the q-Laplace equation.

Cited by

• Gradient higher integrability of bounded solutions to parabolic double-phase systems
• Bounded solutions and interpolative gap bounds for degenerate parabolic double phase problems
• Partial regularity for parabolic systems of double phase type

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• Continuity estimates for degenerate parabolic double-phase equations via nonlinear potentials
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• Hölder regularity for mixed local and nonlocal p-Laplace parabolic equations
• Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate Case