Second order elliptic partial differential equations driven by L\'evy white noise

TL;DR

This paper investigates second order elliptic stochastic partial differential equations driven by Lévy white noise, establishing existence results for solutions and exploring the generalized electric Schrödinger operator with various potentials.

Contribution

It introduces an existence theorem for integral transforms of Lévy white noise and proves the existence of generalized and mild solutions for these elliptic PDEs, expanding the understanding of stochastic PDEs driven by Lévy noise.

Findings

Existence of solutions for elliptic SPDEs driven by Lévy white noise

Development of integral transform techniques for Lévy noise

Analysis of the generalized electric Schrödinger operator with different potentials

Abstract

This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'{e}vy white noise. We first derive an existence theorem for integral transforms of L\'{e}vy white noise and prove the existence of generalized and mild solutions of second order elliptic partial differential equations. Furthermore, we discuss the generalized electric Schr\"odinger operator for different potential functions $V$.