# Venttsel boundary value problems with discontinuous data

## TL;DR

This paper investigates Venttsel boundary value problems with discontinuous coefficients, establishing maximal regularity and strong solvability in Sobolev spaces for both linear and quasilinear cases.

## Contribution

It provides new a priori estimates and proves maximal regularity and solvability results for elliptic Venttsel problems with discontinuous data.

## Key findings

- Established a priori estimates for solutions.
- Proved maximal regularity in Sobolev spaces.
- Demonstrated strong solvability for linear and quasilinear cases.

## Abstract

We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are proved.