BIT Professor Wang Bo makes progress in research of Fully Nonlinear Nirenberg Problem

Recently, Associate Professor Wang Bo from the School of Mathematics and Statistics at Beijing Institute of Technology (BIT), in collaboration with Professor Yanyan Li from Rutgers University and Associate Professor Luc Nguyen from the University of Oxford, published a research paper titled "On the σκ-Nirenberg problem" in the American Journal of Mathematics.

The Nirenberg problem was proposed by Abel Prize winner and member of the United States National Academy of Sciences, L. Nirenberg, in 1969-1970. Since its inception, the problem has garnered significant international attention. Many renowned scholars, including J. Moser (a member of the United States National Academy of Sciences, Wolf Prize laureate), J. -M. Coron (a member of the French Academy of Sciences), S. -Y. A. Chang (an academician of the Chinese Academy of Sciences), Gongqing Zhang (an academician of the Chinese Academy of Sciences), Weiyue Ding (an academician of the Chinese Academy of Sciences), R. Schoen (a member of the United States National Academy of Sciences, Wolf Prize laureate), and Li Yanyan, have made outstanding contributions to this field. To overcome the challenges posed by the lack of compactness in this problem, various notable methods and techniques in nonlinear functional analysis and elliptic partial differential equations, such as Moser iteration, moving plane method, and gluing techniques, have been developed and widely applied to other branches of mathematics.

The σκ-Nirenberg problem is a natural generalization of the classical Nirenberg problem, equivalent to solving a class of fully nonlinear elliptic equations with critical Sobolev exponents on the sphere. The intrinsic difficulties in solving these equations lie in handling the lack of compactness and high nonlinearity. This paper considers the case where k is greater than or equal to n/2. By developing a fully nonlinear Moser Iteration technique, the authors establish a complete blow-up analysis theory, achieving results on the existence and compactness of solutions for this problem. This work extends the results of S.-Y. A. Chang and collaborators for the case k=2, n=4.

Paper link: https://muse.jhu.edu/pub/1/article/917542/pdf

About the author:

Wang Bo, who received joint doctoral training offered by Beijing Normal University and Rutgers University, is a tenured associate professor and doctoral supervisor at BIT. His primary research focuses on fully nonlinear elliptic and parabolic partial differential equations with geometric backgrounds. He has published over 10 papers in journals such as American Journal of Mathematics, Journal of Functional Analysis, Calculus of Variations and Partial Differential Equations, and Journal of Differential Equations. He has also led two projects funded by the National Natural Science Foundation of China and one project funded by the Beijing Natural Science Foundation.