Parabolic boundary Harnack principles in domains with thin Lipschitz complement

2014/01/29 by Arshak Petrosyan, Wenhui Shi, Wenhui shi
Mathematics · #Advanced Harmonic Analysis Research #Boundary (topology) #Complement (music) #Geometric Analysis and Curvature Flows #Harnack's inequality #Harnack's principle #Lipschitz continuity #Nonlinear Partial Differential Equations #Parabolic partial differential equation #math.AP

paper · pdf · doi:10.2140/apde.2014.7.1421

arxiv created 2014/01/29 · openalex publication_date 2014/10/18 · arxiv updated 2015/02/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We prove forward and backward parabolic boundary Harnack principles for nonnegative solutions of the heat equation in the complements of thin parabolic Lipschitz sets given as subgraphs

Citations

• Second Order Parabolic Differential Equations
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian