SIMBa: An interior regularity result for the MEMS problem

Dimecres 29 de novembre se celebrarcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Renzo Bruera Méndez.
Universitat: Universitat Politècnica de Catalunya.

Data: Dimecres, 29 de novembre de 2023.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UPC i Zoom.
Idioma: Anglès.

Títol: An interior regularity result for the MEMS problem.

Resum: In this talk we present an interior regularity result for the class of stable solutions to a semilinear elliptic equation with a singular nonlinearity.
The class of nonlinearities that we consider are real-valued functions defined on [0,1) which are positive, nondecreasing, and whose integral on [0,1) is infinite. This equation is a generalization of a model for the deflection of a dielectric elastic membrane in a microelectromechanical system (MEMS). Solutions to this equation are critical points of an associated energy functional. We say that a solution is stable when the second variation of the energy at the solution is nonnegative. Under a growth assumption on the nonlinearity, we are able to prove that every stable solution is regular up to the optimal dimension, n=6.