Infinite-dimensional elliptic equations and operators of Lévy type

Abstract

CONTENTS Introduction Chapter I. Infinite-dimensional elliptic operators § 1. Lévy's Laplacian § 2. The second-order differential operator generated by Lévy's Laplacian § 3. Differential operators of any even order generated by Lévy's Laplacian § 4. Infinite-dimensional elliptic differential expressions Chapter II. Infinite-dimensional symmetric elliptic operators § 1. The symmetrized Lévy's Laplacian on functions from the domain of the Laplace-Lévy operator § 2. Lévy's Laplacian on functions from the domain of the symmetric Laplace-Lévy 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-Lévy and Poisson-Lévy equations § 2. The Dirichlet problem for the Schrödinger-Lévy 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 Lévy type expressions to obtain the characteristics of processes described by parabolic equations with random coefficients References