We consider Dirichlet problems for the Poisson equation and linear and nonlinear equations with essentially infinite-dimensional elliptic operator (of the Laplace–Lévy type). The continuous dependence of solutions on boundary values and sufficient conditions for increasing the smoothness of solutions are investigated.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 2, pp. 229–236, February, 2012.
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Statkevych, V.M. Investigation of solutions of boundary-value problems with essentially infinite-dimensional elliptic operator. Ukr Math J 64, 262–272 (2012). https://doi.org/10.1007/s11253-012-0643-z
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DOI: https://doi.org/10.1007/s11253-012-0643-z