Abstract
This paper deals with linear stochastic partial differential equations with variable coefficients driven by Lévy white noise. First, an existence theorem for integral transforms of Lévy white noise is derived and the existence of generalized and mild solutions of second order elliptic partial differential equations is proved. Further, the generalized electric Schrödinger operator for different potential functions V is discussed.
Highlights
Since the beginning of studying partial differential equations the Laplacian operator d:= ∂j2 was of great interest in different mathematical theories and applications. j =1For example, the solution of the Poisson equation − u=f www.vmsta.orgD
We study the moment properties of generalized random processes s driven by Lévy white noise L
For a well-defined random process s(φ) = L, G(φ), φ ∈ D(Rd ) we show in Theorem 3 that if Lhas finite β > 0 moment, s has finite βmoment under further conditions on the kernel G
Summary
Since the beginning of studying partial differential equations the Laplacian operator d:= ∂j2 was of great interest in different mathematical theories and applications. j =1For example, the solution of the Poisson equation − u=f www.vmsta.orgD. In [2] it was shown that a convolution operator, with certain properties regarding his integrability, defines a generalized random process, assuming low moment conditions on the Lévy white noise.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call