Regularity of distributional solutions to stochastic acoustic and elastic scattering problems

TL;DR

This paper investigates the well-posedness and regularity of distributional solutions in stochastic acoustic and elastic scattering, emphasizing the influence of the regularity of random media and sources.

Contribution

It establishes the dependence of solution regularity on the regularity of the random medium and source, advancing understanding of stochastic scattering problems.

Findings

Solution regularity depends on the regularity of the random medium.

Solution regularity depends on the regularity of the random source.

Results contribute to the mathematical theory of stochastic scattering.

Abstract

This paper is concerned with the well-posedness and regularity of the distributional solutions for the stochastic acoustic and elastic scattering problems. We show that the regularity of the solutions depends on the regularity of both the random medium and the random source.