Infinite-dimensional elliptic equations and operators of Lévy type
М. Н. Феллер · Russian Mathematical Surveys · 1986
CONTENTS Introduction Chapter I. Infinite-dimensional elliptic operators ??1. L?vy's Laplacian ??2. The second-order differential operator generated by L?vy's Laplacian ??3. Differential operators of any even order generated by L?vy's Laplacian ??4. Infinite-dimensional elliptic differential expressions Chapter II. Infinite-dimensional symmetric elliptic operators ??1. The symmetrized L?vy's Laplacian on functions from the domain of the Laplace-L?vy operator ??2. L?vy's Laplacian on functions from the domain of the symmetric Laplace-L?vy operator ??3. Formally self-adjoint elliptic expressions Chapter III. The solution of boundary-value problems for elliptic equations for functionals defined on function spaces ??1. The Dirichlet problem for the Laplace-L?vy and Poisson-L?vy equations ??2. The Dirichlet problem for the Schr?dinger-L?vy equation ??3. The Riquier problem for a polyharmonic equation Chapter IV. The solubility of boundary-value problems for infinite-dimensional elliptic equations ??1. Equations with constant coefficients ??2. Self-adjoint equations Appendix. An application of L?vy type expressions to obtain the characteristics of processes described by parabolic equations with random coefficients References