Local regularity for fractional heat equations

2017/04/25 by Umberto Biccari, Biccari, Umberto, Mahamadi Warma +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1704.07562

openalex publication_date 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set Ω⊂ℝ^N. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.

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• Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

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