Some Remarks on Solvability of Dirichlet Problem for Laplace Equation in Non-standard Function Spaces

Non-standard grand-Lebesgue and Morrey spaces are considered in this work, together with grand-Sobolev and Morrey–Sobolev spaces generated by them. Dirichlet problems for Laplace equation in different versions are considered in these spaces in a bounded domain of n-dimensional space with sufficiently smooth boundary. These spaces are non-separable, so there arise some questions and differences in problem statements. We conduct a corresponding research and we illustrate the differences concerning the solvability in the classical Sobolev and Hardy spaces in two-dimensional case on the example of circle.