# An Optimal Geometric Condition on Domains for Boundary Differentiability of Solutions of Elliptic Equations

## TL;DR

This paper establishes an optimal geometric condition on domains that ensures solutions to elliptic equations are differentiable at the boundary, advancing understanding of boundary regularity in elliptic PDEs.

## Contribution

It introduces a new geometric condition on domains that guarantees boundary differentiability of elliptic solutions and proves this condition is optimal.

## Key findings

- The geometric condition guarantees boundary differentiability of solutions.
- The condition is proven to be optimal.
- Provides a characterization of boundary regularity for elliptic equations.

## Abstract

In this paper, a geometric condition on domains will be given which guarantees the boundary differentiability of solutions of elliptic equations, that is, the solutions are differentiable at any boundary point. We will show that this geometric condition is optimal.