Hölder regularity results for parabolic nonlocal double phase problems

2021/12/08 by J. Giacomoni, D. Kumar, Giacomoni, J. +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.04287

openalex publication_date 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we obtain higher Hölder regularity results for weak solutions to nonlocal problems driven by the fractional double phase operator \mc L u(x):=amp;2 \rm P.V. ∫_{\mathbb R^N} \frac|u(x)-u(y)|^p-2(u(x)-u(y))|x-y|^N+ps₁dy amp;+2 \rm P.V. ∫_{\mathbb R^N} a(x,y) \frac|u(x)-u(y)|^q-2(u(x)-u(y))|x-y|^N+qs₂dy, where 1

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• Higher Hölder regularity for fractional (p,q)-Laplace equations

Related

• Hölder regularity for weak solutions to nonlocal double phase problems
• Hölder regularity for nonlocal double phase equations
• Regularity of weak solutions for mixed local and nonlocal double phase parabolic equations
• Gradient regularity for nonlocal double phase equations
• Hölder regularity for degenerate parabolic double-phase equations