Abstract elliptic and parabolic equat{\i}ons in Morrey spaces and applications

TL;DR

This paper investigates the properties of differential-operator equations in Morrey spaces, establishing their role as generators of analytic semigroups and exploring maximal regularity for elliptic and parabolic equations with applications to specific boundary value problems.

Contribution

It demonstrates that differential operators in Morrey spaces generate analytic semigroups and establishes maximal regularity for related elliptic and parabolic equations, with applications to Wentzell-Robin and degenerate problems.

Findings

Differential operators generate analytic semigroups in Morrey spaces.

Maximal regularity properties are established for elliptic and parabolic equations.

Applications include boundary value problems of Wentzell-Robin type and degenerate parabolic equations.

Abstract

We presents the study the separability properties for differential-operator equations in Morrey spaces. We prove that the corresponding differential operator is a generator of analytic semigroup in vector-valued Morrey spaces. Moreover, maximal regularity properties of corresponding parabolic equation {\i}s obtained. In applications, the maximal regularity properties of Wentzell-Robin type problem for elliptic equations and mixed value problem for degenerate parabolic equations in Morrey spaces are derived.