Perturbation theory for the parabolic Regularity and Neumann problem

2024/08/22 by Martin J. Ulmer, Ulmer, Martin · 1 citation
Computer Science · Mathematics · #35K10 #35K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2408.12529

openalex publication_date 2024/08/22 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/28

Abstract

We show small and large Carleson perturbation results for the parabolic Regularity boundary value problem with boundary data in L_1,1/2^p and small Carelson perturbation results for the Neumann problem with boundary data in L^p. The operator we consider is L:=∂_t -div(A∇⋅) and the domains are parabolic cylinders Ω=O×ℝ, where O is a Lipschitz domain.

Cited by

• The L^p regularity problem for parabolic operators with transversally independent coefficients

Related

• The L^p regularity problem for parabolic operators
• A relation between the Dirichlet and the Regularity problem for Parabolic equations
• The L^p regularity problem for parabolic operators with transversally independent coefficients
• On the regularity problem for parabolic operators and the role of half-time derivative
• Parabolic Regularity and Dirichlet boundary value problems