May 26th, 2021 the next seminar of the department “Equations of Mathematical Physics” was held.
At the seminar, with a report on the topic “The Dirichlet problem for of semi–linear elliptic equations of the second order” Ph.D in physical and mathematical sciences Shahla Shukurova delivered a speech. During the report, a strong solvability of the Dirichlet problem for a class of semilinear elliptic equations of the non-divergence form of second order was investigated. For this problem, the existence of a solution in Sobolev spaces was proved when the norm of the right-hand side of this equation is sufficiently small. In the proof of this theorem, Schauder’s theorem on a continuous mapping of a convex and compact set in a Banach space was used.
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