# Free boundary value problems for abstract elliptic equations and applications

## TL;DR

This paper investigates free boundary value problems for elliptic differential-operator equations with variable coefficients, establishing uniform maximal regularity and Fredholm properties in vector-valued Hölder spaces.

## Contribution

It introduces new results on the regularity and Fredholmness of free boundary problems for elliptic equations with variable coefficients.

## Key findings

- Established uniform maximal regularity in vector-valued Hölder spaces
- Proved Fredholmness of the free boundary value problem
- Extended theory to variable coefficient elliptic equations

## Abstract

Free bondary value problem for elliptic differential-operator equations with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued Holder spaces.