On boundary value problems for an improperly elliptic equation in a circle
V. P. Burskiiab, E. V. Lesinac
a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, 141701 Russia
b RUDN University, Moscow, 117198 Russia
c Donetsk National Technical University, Pokrovsk, Donetsk oblast, 85300 Ukraine
The paper considers the solvability of the first, second, and third boundary value problems, as well as one problem with a directional derivative, in a bounded domain for a scalar improperly elliptic differential equation with complex coefficients. More detailed consideration is given to a model case in which the domain is a unit disk and the equation does not contain lower-order terms. For each of these problems, the classes of boundary data for which there exists a unique solution in the ordinary Sobolev space are characterized. In a typical case, such classes turned out to be the spaces of function with exponentially decreasing Fourier coefficients. These problems have been the subject of several previous publications of the authors, and, in this article, the earlier-obtained results have been collected together and are presented from a unified point of view.
improperly elliptic equations, boundary value problems in a disk, Sobolev spaces, Dirichlet problem, Neumann problem, Poincaré problem, third boundary value problem.
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1306–1321
V. P. Burskii, E. V. Lesina, “On boundary value problems for an improperly elliptic equation in a circle”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1351–1366; Comput. Math. Math. Phys., 60:8 (2020), 1306–1321
Citation in format AMSBIB
\by V.~P.~Burskii, E.~V.~Lesina
\paper On boundary value problems for an improperly elliptic equation in a circle
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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