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Information × Registration Number 0222U000119, 0121U111851 , R & D reports Title Regularity for solutions of elliptic and parabolic equations and asymptotic properties of metric spaces at infinity popup.stage_title Head Bilet Viktoriia V., Кандидат фізико-математичних наук Registration Date 03-01-2022 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description2 The project focuses on the development of methods for studying the qualitative properties of solutions of quasilinear elliptic and parabolic equations with nonstandard growth conditions and studying the asymptotic behavior of general metric spaces at infinity. We describe the class of graphs for which all metric spaces with diametrical graphs belonging to this class are ultrametric. It is shown that a metric space is ultrametric iff the diametrical graph of the metric is either complete multipartite or empty. A refinement of the last result is obtained for totally bounded spaces. Moreover, using complete multipartite graphs we characterize the compact ultrametrizable topological spaces. We study nonnegative weak solutions of a quasilinear parabolic equations in a divergent form one of the model cases of which is anisotropic evolution p-Laplacian equation. New precise integral estimates, pointwise estimates near an isolated singularity and condition of the removability of isolated singularity were obtained. Product Description popup.authors Savchenko Mariia O. popup.nrat_date 2022-03-09 Close