# Differential operators in exterior domain and application

## TL;DR

This paper studies elliptic and parabolic equations with variable coefficients in exterior domains, establishing boundary value problem properties and well-posedness for various related problems.

## Contribution

It introduces new results on the separability and well-posedness of boundary value problems for elliptic and parabolic equations with variable coefficients in exterior domains.

## Key findings

- Well-posedness of boundary value problems established
- Separability properties of elliptic equations proved
- Well-posedness of various parabolic problems derived

## Abstract

The abstract elliptic and parabolic equations on exterior domain are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and well-posedness of the Cauchy problem for parabolic equations are established. In application, the well-posedness of Wentzell-Robin type mixed probem for parabolic equation, Cauchy problem for anisotropic parabolic equations and system of parabolic equations are derived