Investigation of solutions of boundary-value problems with essentially infinite-dimensional elliptic operator - Statkevych, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We consider Dirichlet problems for the Poisson equation and linear and nonlinear equations with essentially infinite-dimensional elliptic operator (of the Laplace -Levy type). The continuous dependence of solutions on boundary values and sufficient conditions for increasing the smoothness of solutions are investigated.