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Smoothness of generalized solutions to the Dirichlet problem for strongly elliptic functional differential equations with orthotropic contractions on the boundary of adjacent subdomains

A. L. Tasevich<sup>ab

a</sup> RUDN University, Moscow, Russia
^b Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Moscow, Russia

Abstract: The paper is devoted to the study of the smoothness of generalized solutions of the first boundary-value problem for a strongly elliptic functional differential equation containing orthotropic contraction transformations of the arguments of the unknown function in the leading part. The problem is considered in a circle, the coefficients of the equation are constant. Orthotropic contraction is understood as different contraction in different variables. Conditions for the conservation of smoothness on the boundaries of neighboring subdomains formed by the action of the contraction transformation group on a circle are found in explicit form for any right-hand side from the Lebesgue space.

Keywords: strongly elliptic functional differential equation, orthotropic contraction of arguments, smoothness of generalized solutions.

UDC: 517.956.223

DOI: 10.22363/2413-3639-2023-69-1-152-165