Comparability and regularity estimates for symmetric nonlocal Dirichlet forms

2011/09/30 by Bartłomiej Dyda, Moritz Kaßmann, Dyda, Bartłomiej +1
Computer Science · Mathematics · #31B05 #35B05 #35B45 #35R05 #47G20 #60J75 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1109.6812

openalex publication_date 2011/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to study comparability of nonlocal Dirichlet forms. We provide sufficient conditions on the kernel for local and global comparability. As an application we prove a-priori estimates in Hölder spaces for solutions to integrodifferential equations. These solutions are defined with the help of symmetric nonlocal Dirichlet forms.

Citations

• Transition Probabilities for Symmetric Jump Processes
• Hitchhiker's guide to the fractional Sobolev spaces

Related

• Remarks on the nonlocal Dirichlet problem
• Robust estimates for elliptic nonlocal operators on doubling spaces
• Optimal boundary regularity for mixed local and nonlocal equations
• Regularity results for nonlocal equations and applications
• Regularity for fully nonlinear equations driven by spatial-inhomogeneous nonlocal operators