Abstract:
We consider the Dirichlet problem for
harmonic functions on two-dimensional
stratified sets, which are assumed for
simplicity to be complexes. We show that
under certain conditions this problem is
Fredholm in the Hölder space and
in weighted Hölder spaces of functions
satisfying the Hölder condition outside
any neighbourhood of the vertex set
of the complex and admitting power singularities.
We also study the power-logarithmic asymptotics
of solutions at these vertices.
This paper was written with the support of the International Project (0113RK01031) of the Ministry of Science and Education of the Republic of Kazakhstan.
This publication is cited in the following 2 articles:
L. A. Kovaleva, A. P. Soldatov, “Dirichlet problems for functions that are harmonic on a two-dimensional net”, J. Math. Sci. (N. Y.), 257:1 (2021), 41–47
Andreyev A.A., Padchenko V.P., Kozlova E.A., “To the 70Th Anniversary of Professor Alexander Pavlovich Soldatov”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:1 (2018), 15–22