Recent Advances in Brezis-Nirenberg Problem
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Juncheng Wei
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Chinese University of Hong Kong
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Hong Kong
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Yuanze Wu
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Yunnan Normal University
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Peoples Rep of China
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Introduction:
| | The Brezis-Nirenberg problem is a classical problem in the field of nonlinear partial differential equations (PDEs) and elliptic boundary value problems. It was introduced by Haïm Brezis and Louis Nirenberg in their seminal 1983 paper. The problem is concerned with the existence and properties of solutions to certain semilinear elliptic equations with critical nonlinearities, particularly in the context of the Sobolev embedding theorem. For over forty years, the Brezis-Nirenberg problem has a profound influence on the study of nonlinear elliptic equations, particularly those involving critical exponents. It has inspired extensive research in areas such as: Variational methods and critical point theory, Concentration-compactness principles, and Geometric PDEs and Yamabe-type problems. The problem remains a central topic in modern PDE theory and continues to be actively studied. In fact, one year before his death, Brezis gave a list of his ``favorite open problems", which he described as challenges he had "raised throughout his career and has resisted so far". The first Open Problem on his list is the Brezis-Nirenberg Problem on a three-dimensional ball. The purpose of this special session is to report the most important and advanced studies on Brezis-Nirenberg Problem in last five years.
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