On linear Schrödinger parabolic problems in Morrey spaces

2024/07/23 by Cholewa, Jan W., Rodriguez-Bernal, Anibal · 1 citation
#35K30 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.16605

Abstract

We consider parabolic Schrödinger 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.

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• Evolution equation with fractional Schrödinger operators: monotonicity and exponential decay of solutions in Morrey spaces

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