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Information × Registration Number 0226U000022, (0125U002854) , R & D reports Title Solvability and regularity of solutions to mathematical physics equations with non-standard and integro-differential structure popup.stage_title Неперервність розв’язків анізотропного N-Лапласіана та існування розв’язків нормально розв‘язних інтегро - диференціальних крайових задач Head Savchenko Mariia O., Кандидат фізико-математичних наук Registration Date 01-01-2026 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description1 Development of new theoretical approaches and adaptation of modern methods of nonlinear analysis to study the regularity of solutions of elliptic and parabolic equations with non-standard structure, and extension of existing results on the conditions for solvability of integral-differential nonlinear boundary value problems for improvement of the analytical apparatus and further advancement of the theoretical methods in the study of complex mathematical models. popup.description2 Object of the research is the anisotropic elliptic N-Laplacian and a linear Noetherian integro-differential boundary value problem. The aim of the research is to adapt modern methods for studying the regularity of solutions to a class of anisotropic elliptic equations in order to obtain continuity conditions for solutions in terms of the Wolff potential. The study also envisages the construction of constructive existence conditions and the development of algorithms for finding solutions to integro-differential boundary value problems that are not resolved with respect to the derivative. Research methods include the adapted Kilpeläinen–Malý iteration technique, the pseudoinversion apparatus (the Moore–Penrose pseudoinverse operator), methods for solving matrix equations, regularization methods for ill-posed boundary value problems, and the least squares method. The obtained results are of a fundamental nature and are aimed at the further development of modern analytical methods for nonlinear and integro-differential equations. Within the framework of the study, the Kilpeläinen–Malý iteration technique was adapted to establish continuity conditions for solutions of the anisotropic elliptic N-Laplacian; the corresponding conditions are formulated in terms of the Wolff potential. In addition, the analytical framework for integro-differential boundary value problems not resolved with respect to the derivative was further developed, in particular, conditions for their regularization were identified and constructive criteria for the existence of solutions were formulated. Product Description popup.authors Vlada O. Kuzmina popup.nrat_date 2026-01-01 Close