On linear Schr\"odinger parabolic problems in Morrey spaces

TL;DR

This paper studies parabolic Schr"odinger equations with fractional elliptic operators in Morrey spaces, establishing stability and perturbation results that extend existing theory using a new abstract perturbation approach.

Contribution

It introduces a general perturbation framework for Schr"odinger problems in Morrey spaces, preserving properties and ensuring solution stability under perturbations.

Findings

Properties of Schr"odinger equations are preserved under perturbations.

Solutions depend continuously on perturbations.

A new abstract perturbation method broadens existing results.

Abstract

We consider parabolic Schr\"odinger type equations associated to fractional powers of uniformly elliptic 2m-order operators with constant coefficients. Potentials and initial data are considered in suitable Morrey spaces. By means of perturbation techniques we prove that several properties of the problem with no potential are preserved. We also prove continuous dependence of solutions with respect to perturbations. To carry out the analysis a general abstract perturbation approach is developed, which broadens the results known in the literature.