# On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains

## TL;DR

This paper investigates the regularity of solutions to nonlocal Venttsel' problems within polygonal and piecewise smooth two-dimensional domains, providing foundational insights into their mathematical properties.

## Contribution

It establishes regularity results for nonlocal Venttsel' problems in complex two-dimensional domains, advancing understanding of their mathematical behavior.

## Key findings

- Regularity results for solutions in polygonal domains
- Extension of Venttsel' problem analysis to nonlocal cases
- Mathematical framework for nonlocal boundary conditions

## Abstract

We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains.