Local Hölder continuity for fractional nonlocal equations with general growth

2021/12/28 by Sun‐Sig Byun, Hyojin Kim, Byun, Sun-Sig +3 · 4 citations
Mathematics · #35B65 #35D30 #35R11 #47G20 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.13958

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

Abstract

We study generalized fractional p-Laplacian equations to prove local boundedness and Hölder continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincaré inquality.

Cited by

• Regularity for mixed-order nonlinear fractional equations with degenerate coefficients
• Higher Hölder regularity for fractional (p,q)-Laplace equations
• Nonlocal Harnack inequality in a disconnected region
• Fractional Orlicz-Sobolev embeddings into Campanato type spaces

Related

• A perturbative approach to Hölder continuity of solutions to a nonlocal p-parabolic equation
• Hölder regularity for fractional p-Laplace equations
• Nonlocal equations with kernels of general order
• Global Hölder regularity for the fractional p-Laplacian
• Recent progresses in the theory of nonlinear nonlocal problems