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SUMMARY:Renzo Bruera Méndez (Universitat Politècnica de Catalunya)
DTSTART:20231129T120000Z
DTEND:20231129T130000Z
DTSTAMP:20260423T021649Z
UID:SIMBa/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIMBa/17/">A
 n interior regularity result for the MEMS problem</a>\nby Renzo Bruera Mé
 ndez (Universitat Politècnica de Catalunya) as part of Barcelona Mathemat
 ics Informal Seminar (SIMBa)\n\nLecture held in UPC FME\, Aula 005.\n\nAbs
 tract\nIn this talk we present an interior regularity result for the class
  of stable solutions to a semilinear elliptic equation with a singular non
 linearity. The class of nonlinearities that we consider are real-valued fu
 nctions defined on [0\,1) which are positive\, nondecreasing\, and whose i
 ntegral on [0\,1) is infinite. This equation is a generalization of a mode
 l for the deflection of a dielectric elastic membrane in a microelectromec
 hanical system (MEMS).\n\nSolutions to this equation are critical points o
 f an associated energy functional. We say that a solution is stable when t
 he second variation of the energy at the solution is nonnegative. Under a 
 growth assumption on the nonlinearity\, we are able to prove that every st
 able solution is regular up to the optimal dimension\, n=6.\n
LOCATION:https://researchseminars.org/talk/SIMBa/17/
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