{"id":31138,"date":"2020-03-04T15:09:03","date_gmt":"2020-03-04T11:09:03","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?p=31138"},"modified":"2020-03-04T15:09:05","modified_gmt":"2020-03-04T11:09:05","slug":"a-joint-seminar-of-the-department-differential-equations-and-the-department-equations-of-mathematical-physics-on-the-topic-on-strong-solutions-of-nonlinear","status":"publish","type":"post","link":"https:\/\/www.imm.az\/exp\/2020\/03\/04\/a-joint-seminar-of-the-department-differential-equations-and-the-department-equations-of-mathematical-physics-on-the-topic-on-strong-solutions-of-nonlinear\/","title":{"rendered":"A joint seminar of the department \u201cDifferential Equations\u201d and the department \u201cEquations of Mathematical Physics\u201d on the topic \u201cOn strong solutions of nonlinear (semi-linear) elliptic equations of the second order\u201d was held"},"content":{"rendered":"

March 4th, 2020 the joint seminar of the department \u201cDifferential Equations\u201d<\/em><\/strong> \u00a0and the department \u201cEquations of Mathematical Physics\u201d<\/em><\/strong> was held.<\/p>\n

At the seminar, with a report on the topic \u201cOn strong solutions of nonlinear (semi-linear) elliptic equations of the second order\u201d<\/strong> the Doctor of Mathematical Sciences Rabil\u00a0 Amanulla oglu Amanov<\/strong> 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 \u00a0 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 \u00a0Bernstein. The considered method of\u00a0 proof\u00a0 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.<\/p>\n