A Survey of Results of St. Petersburg State University Research School on Nonlinear Partial Differential Equations. I

IF 0.4 Q4 MATHEMATICS

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI:10.1134/s1063454124010035

D. E. Apushkinskaya, A. A. Arkhipova, A. I. Nazarov, V. G. Osmolovskii, N. N. Uraltseva

引用次数: 0

Abstract

The article contains a review of the most important results obtained in the framework of the St. Petersburg State University Research School on Nonlinear PDEs (the O.A. Ladyzhenskaya–N.N. Uraltseva School). The main attention is paid to the works carried out at the university over the past 50 years. The first part of the review concerns the solvability and qualitative properties of solutions to boundary value problems for the second order scalar quasilinear elliptic and parabolic equations, as well as variational problems. The planned second part of the review will include sections on fully nonlinear equations and systems of equations, and on free boundary problems.

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圣彼得堡国立大学非线性偏微分方程研究学院成果概览》。I

摘要文章回顾了在圣彼得堡国立大学非线性PDE研究学院（O.A. Ladyzhenskaya-N.N. Uraltseva学院）框架内取得的最重要成果。主要关注的是过去 50 年来在该大学开展的工作。综述的第一部分涉及二阶标量准椭圆和抛物方程的边界值问题的可解性和解的定性，以及变分问题。计划中的第二部分将包括关于全非线性方程和方程组以及自由边界问题的章节。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Vestnik St Petersburg University-Mathematics MATHEMATICS-

CiteScore

0.70

自引率

50.00%

发文量

期刊介绍： Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.