Solutions of linear elliptic equations in Gauss-Sobolev spaces

Pao-Liu Chow
2012 Communications on Stochastic Analysis  
The paper is concerned with a class of linear elliptic equations in a Gauss-Sobolev space setting. They arise from the stationary solutions of the corresponding parabolic equations. For nonhomogeneous elliptic equations, under appropriate conditions, the existence and uniqueness theorem for strong solutions is given. Then it is shown that the associated resolvent operator is compact. Based on this result, we shall prove a Fredholm Alternative theorem for the elliptic equation and a
more » ... and a Sturm-Liouville type of theorem for the eigenvalue problem of a symmetric elliptic operator. Received 2012-8-26; Communicated by the editors. 2000 Mathematics Subject Classification. Primary 60H; Secondary 60G, 35K55, 35K99, 93E.
doi:10.31390/cosa.6.3.08 fatcat:ki3j6qkasfbtrijbnzvzjwhsse