Anisotropic Function Spaces and Elliptic Boundary Value Problems

TL;DR

This paper investigates anisotropic function spaces, specifically Bessel potential and Besov spaces, and applies their properties to solve elliptic boundary value problems with directional regularity considerations.

Contribution

It introduces and analyzes anisotropic Bessel potential and Besov spaces, establishing their properties and applying them to elliptic boundary value problems.

Findings

Established basic properties of anisotropic function spaces

Applied anisotropic spaces to elliptic boundary value problems

Enhanced understanding of directional regularity in PDEs

Abstract

In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along with applications to elliptic boundary value problems.