1. Science Building, #225, Yonsei University
연세대학교 응용해석 및 계산센터 세미나
Partial Differential Equations
and Applied Mathematics Seminar
Title
Minimal energy solutions to the fractional Lane-Emden system: Existence and singularity formation
Speaker
김승혁 박사
Affiliation
 고등과학원
Date
Dec 28th, Wed., 4:00~ 5:00 Pm
Location
Science Building, #225, Yonsei University
Abstract
In the last decades, nonlinear elliptic systems have attracted researchers because of their practicality and profound mathematical depth. Also, recent development of the field allowed one to treat equations with a large class of integro-differential operators other than local elliptic operators such as the Laplacian or its square. In this talk, we consider minimal energy solutions of the fractional Lane-Emden equation, one of the simplest nonlocal Hamiltonian systems. Especially, we discuss their existence and asymptotic behavior as the exponents of the nonlinear terms approach to so called the Sobolev critical hyperbola. The close relationship between the system and the Hardy-Littlewood-Sobolev inequality is also to be explained. This work is collaborated with Woocheol Choi (KIAS, Korea).