Continuity of solutions to equations with weakly singular nonlocal operators

2023/11/26 by Jarohs, Sven, Kassmann, Moritz, Weth, Tobias
#35B65 #35R09 #47G20 #60J75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.15337

Abstract

We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions are continuous, and we provide a uniform a-priori estimates for the modulus of continuity. In contrast to earlier works, we allow the nonlocal operators to be highly anisotropic and weakly singular, and we allow the associated kernel functions to vanish close to the singularity.

Related

• Regularity theory for singular nonlocal diffusion equations
• Singularities of solutions of nonlocal nonlinear equations
• Nonlocal equations with kernels of general order
• Nonlocal operators in divergence form and existence theory for integrable data
• Regularity for nonlocal problems with non-standard growth