Regular general seminar of the Institute of Mathematics was held

18.03.2026 /

A regular general seminar of the Institute of Mathematics of the Ministry of Science and Education of the Republic of Azerbaijan was held on March 18, 2026. At the seminar, Head of the Differential Equations Laboratory Professor Farman Mammadov, DSc in Physics and Mathematics, made a presentation "On the strong solvability of the Dirichlet problem for second-order quasilinear elliptic equations."
The speaker first presented an explanatory chronology of the key results achieved in global literature. Subsequently, against the backdrop of these findings, the authors' own research results were discussed, providing a comparative analysis with other established results.
There is extensive literature regarding the existence and uniqueness of solutions to the first boundary value problem for second-order quasilinear elliptic and parabolic equations. The famous monographs by Ladyzhenskaya, Uraltseva, D. Gilbarg, and N. Trudinger were cited as primary sources for familiarizing oneself with classical results in this field.
It was noted that since the 1970s, the solvability of quasilinear elliptic equations had begun to develop more systematically and deeply. The significant contributions of scholars such as Stampacchia, Bernstein, Boccardo, Murat, Poretta, Amann, Crandall, Segura de Leon, Lions, Ambrosetti, Rabinowitz, Pohozaev, and others were specifically highlighted.
In conclusion, the seminar participants asked the speaker their questions, and an extensive discussion on the topic was held.