Today the regular Institute seminar was held. In the seminar of the Institute of Mathematics and Mechanics of ANAS the leading researcher of the department “Functions Theory” Sarvan Tahmaz oglu Huseynov gave a talk «Quality properties of solutions of second order degenerate equations of elliptic and parabolic types».

The report is devoted to the first boundary value problem for second order uniformly degenerating divergent elliptic equations and also Holder continuity of solutions, density of smooth functions in a weighted Sobolev space, Holder continuity and Harnack inequality for the solutions of p-Laplacian with Mackenhoupt weight degenerated into a part of the domain, Holder continuity and Harnack inequality for the solutions of an elliptic equation uniformly degenerated into parts of the domain of elliptic equation containing p-Laplacian. Holder continuity and Harnack inequality for the solutions of uniformly degenerating into a part of the domain of elliptic (p,q)-Laplacian are also studied. Furthermore, the Dirichlet problem for a class of nonuniformly degenerating elliptic and parabolic equations of second order is studied. The Holder continuity and Harnack inequality was studied for the solutions of nonuniformly degenerated parabolic equations.

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