Seminari SIMBa: An interior regularity result for the MEMS problem

El proper dimecres 29 de novembre, després de la conferència de l'IMTech, torna a la FME el seminari interuniversitari SIMBA. Aquest seminari, adreçat a joves matemàtics i impulsat per la UPC i la BGSMath, entre d'altres, ofereix una xerrada cada dues setmanes, normalment per part d'un doctorand, dirigida a altres doctorands i a estudiants de grau i màster. En podeu trobar més informació a https://www.ub.edu/simba/en/

Conferenciant: Renzo Bruera Méndez (Universitat Politècnica de Catalunya)
Títol: An interior regularity result for the MEMS problem.
Dia i hora: Dimecres 29 de novembre a les 13:20.
Lloc: Aula 005 de la FME i Zoom.

Abstract: 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.