2025/12/01 by Philipp Svinger, Marvin Weidner, Svinger, Philipp +1
Mathematics · #35B65 #35K08 #47G20 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2512.01919
openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
In this article we establish the optimal Cs boundary regularity for solutions to nonlocal parabolic equations in divergence form in C1,α domains and prove a higher order boundary Harnack principle in this setting. Our approach applies to a broad class of nonlocal operators with merely Hölder continuous coefficients, but our results are new even in the translation invariant case. As an application, we obtain sharp two-sided estimates for the associated Dirichlet heat kernel. Notably, our estimates cover nonlocal operators with time-dependent coefficients, which had remained open in the literature.