ABSTRACT OF THE TALK
In this talk, we discuss some nonlinear eigenvalue problems on a bounded smooth domain of $R^n$ with homogeneous Dirichlet boundary condition, where the nonlinearity is a positive nondecreasing convex function which is singular, that is, it tends to infinity at a finite value. Our study is motivated by a simplified Micro-Electromechanical Systems (MEMS) device model. We extend or improve some qualitative and quantitative results for the MEMS modeling to a general setting, which help us to understand more about the influence of the permittivity profile on the pull-in voltage and the quenching phenomenon. We investigate also the regularity of the corresponding extremal solution. Finally some discussion will be done for the problem with nonlocal term.
Feng Zhou is a professor of mathematics at ECNU. His current interests include partial differential equations and calculus of variations, in particular asymptotic analysis for nonlinear elliptic problems.