Optimal Boundary Regularity for Uniformly Degenerate Elliptic Equations

TL;DR

This survey explores the best possible regularity results for solutions to uniformly degenerate elliptic equations, focusing on boundary behavior and establishing H"older continuity of solutions and derivatives.

Contribution

It provides a comprehensive overview of boundary regularity results for uniformly degenerate elliptic equations, highlighting optimal regularity conditions.

Findings

Solutions are H"older continuous up to the boundary.

Derivatives of solutions also exhibit H"older continuity.

The paper identifies conditions for optimal boundary regularity.

Abstract

In this survey paper, we study the optimal regularity of solutions to uniformly degenerate elliptic equations in bounded domains and establish the H\"older continuity of solutions and their derivatives up to the boundary.