A quantitative constant rank Theorem for quasiconcave solutions to fully nonlinear elliptic equations

Time: April 2, 2022, 14:00-16:00

Tencent Meeting ID: 571 885 125

Lecturer: Professor Lu Xu, Hunan University

Abstract: We investigate a class of fully nonlinear elliptic equations, which satisfy the structural condition previously posed by Bianchini-Longinetti-Salani in 2009. By establishing a novel differential inequality, we prove a weak Harnack inequality for the principal curvatures of the level surfaces of the solutions. This result is indeed a quantitative version of the constant rank theorem showed by Guan-Xu in 2013.

Biography:

Lu Xu is a professor and Ph.D. supervisor from School of Mathematics, Hunan University. She received her undergraduate degree from the Department of Mathematics, East China Normal University in 2000 and her sciencePhD in 2006. She is mainly engaged in the research of elliptic partial differential equations and geometric analysis, and has made innovative progresses in the study of convexity of solutions of completely nonlinear elliptic partial differential equations. Her research papers have been published in Crelle’s journal, JFA, Adv. Math, IUMJ, CVPDE, JDE and other famous international journals. She is also the chair of three projects of the National Natural Science Foundation of China and the Hunan Provincial Natural Science Outstanding Youth Fund.

Sharp existence of standing waves for a class of scalar field equations involving mixed fractional Laplacians

Time: 2 April 2022, 16:00-18:00

Tencent Meeting ID: 244 966 810

Lecturer: Luo Tingjian, Associate Professor, Guangzhou University

Abstract: In this talk, we will introduce a progress on the sharp existence results related with a class of scalar field equations involving mixed fractional Laplacians with different orders. Our study includes the case when one operator is local and the other one is non-local. This type of equations arises in various fields ranging from biophysics to population dynamics.

Biography:

Tingjian Luo is an associate professor of School of Mathematics and Information Science, Guangzhou University. He received his undergraduate degree from the School of Mathematics and Computer Science, Hunan Normal University in 2008 and his PhD in Science from Université de Franche-Comté, France, in 2014. He is mainly engaged in research on variational methods and their applications to partial differential equations. He has published papers in international journals such as Proc. London. Math.Soc., J. Diff. Equa., Z. Angew. Math. Phys. Andhe has also presided over one National Natural Science Foundation of China Youth Project and one Guangdong Provincial Natural Science Foundation Doctoral Initiation Project.

Edited by：Liu Kexi, Li Tiantian

Source: School of Natural Sciences