Remarks on the maximal regularity for parabolic boundary value problems with inhomogeneous data

2025/11/03 by Chen, Hui, Liang, Su, Tsai, Tai-Peng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01230

Abstract

Inspired by Ogawa-Shimizu [JEE 2022] and Chen-Liang-Tsai [IMRN 2025] on the second and first order derivative estimates of solution of heat equation in the upper half space with boundary data in homogeneous Besov spaces, we extend the estimates to any order of derivatives, including fractional derivatives.

Citations

• Poisson kernel and blow-up of the second derivatives near the boundary for Stokes equations with Navier boundary condition
• Maximal L¹-regularity and free boundary problems for the incompressible Navier-Stokes equations in critical spaces
• Maximal L¹-regularity for parabolic initial-boundary value problems with inhomogeneous data
• Local regularity near boundary for the Stokes and Navier-Stokes equations
• Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space

Related

• Maximal L¹-regularity for parabolic initial-boundary value problems with inhomogeneous data
• A note on Besov regularity for parabolic initial boundary value problems
• Local regularity for fractional heat equations
• Parabolic problems with general Wentzell boundary conditions and\n diffusion on the boundary
• Maximal parabolic regularity for divergence operators including mixed boundary conditions