Hölder regularity for degenerate parabolic double-phase equations

We prove that bounded weak solutions to degenerate parabolic double-phase equations of \(p\)-Laplace type are locally H\"older 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 equat...

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Published in:arXiv.org 2024-04
Main Authors: Kim, Wontae, Moring, Kristian, Särkiö, Lauri
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Laplace equation
Mathematical analysis
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description We prove that bounded weak solutions to degenerate parabolic double-phase equations of \(p\)-Laplace type are locally H\"older 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.
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subjects Laplace equation
Mathematical analysis
title Hölder regularity for degenerate parabolic double-phase equations
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