Boundary Hölder gradient estimates for parabolic p-Laplace type equations

2025/06/01 by Se-Chan Lee, Lee, Se-Chan, Yuanyuan Lian +5 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2506.01018

Abstract

In this paper, we study the boundary regularity for viscosity solutions of parabolic p-Laplace type equations. In particular, we obtain the boundary pointwise C^1,α regularity and global C^1,α regularity.

Citations

• Time derivative estimates for parabolic p-Laplace equations and applications to optimal regularity
• Pointwise regularity for locally uniformly elliptic equations and applications
• Second order Sobolev regularity results for the generalized p-parabolic equation
• Boundary pointwise regularity for fully nonlinear parabolic equations and an application to regularity of free boundaries
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• Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity
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• Gradient Holder regularity for parabolic normalized p(x,t)-Laplace equation
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• On viscosity and weak solutions for non-homogeneous p-Laplace equations
• Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian
• Hölder gradient estimates for parabolic homogeneous p-Laplacian equations
• Small Perturbation Solutions for Parabolic Equations
• A new proof for the equivalence of weak and viscosity solutions for the p-Laplace equation
• Existence results for parabolic problems related to fully non linear operators degenerate or singular

Cited by

• Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations
• Harnack inequality for degenerate fully nonlinear parabolic equations

Related

• Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations
• H "older gradient estimates for a class of singular or degenerate\n parabolic equations
• Improved regularity for the parabolic normalized p-Laplace equation
• Hölder gradient estimates for parabolic homogeneous p-Laplacian equations
• Gradient Holder regularity for parabolic normalized p(x,t)-Laplace equation