On trace theorems for weighted mixed-norm Sobolev spaces and applications

DOI10.1515/9783110792720-003arXiv2205.04941OpenAlexW4375945768MaRDI QIDQ6060174

Author name not available (Why is that?)

Publication date: 3 November 2023

Published in: Potentials and Partial Differential Equations (Search for Journal in Brave)

Abstract: We prove trace theorems for weighted mixed norm Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the power in the weight function and the integrability power for the integration with respect to the vertical variable but not on the integrability powers for the integration with respect to the horizontal ones. They are new even in the un-weighted case and they recover classical results in the case of un-mixed norm spaces. The work is motivated by the study of regularity theory for solutions of elliptic and parabolic equations with anisotropic features and with non-homogeneous boundary conditions. The results provide an essential ingredient to the study of fractional elliptic and parabolic equations in divergence form with measurable coefficients.

Full work available at URL: https://arxiv.org/abs/2205.04941

zbMATH Keywords

boundary value problems trace theorems singular and degenerate coefficients mixed-norm Besov spaces weighted mixed-norm Sobolev spaces

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate elliptic equations (35J70) Singular elliptic equations (35J75)