March 4th, 2020 the joint seminar of the department “Differential Equations”  and the department “Equations of Mathematical Physics” was held.

At the seminar, with a report on the topic “On strong solutions of nonlinear (semi-linear) elliptic equations of the second order” the Doctor of Mathematical Sciences Rabil  Amanulla oglu Amanov delivered a speech. During the report, when a certain growth condition was imposed on the nonlinear part, the existence of a strong solution of the second-order nonlinear elliptic equation in the Sobolev space   was considered. The proof of existence was carried out if the solution belongs to a certain Lebesgue class with respect to the spatial variable. Examples are given that show the accuracy of the conditions imposed; the results obtained are presented as a generalization of the known results of  Bernstein. The considered method of  proof  belongs to S.I. Pokhozhaev. The aim of the study is to apply the results to parabolic equations and to study the strong solvability of the problem under the condition of summability of a lower order.

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