Second order elliptic partial differential equations driven by Lévy white noise

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 $V$.