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SUMMARY:Xavier Cabre (ICREA and Universitat Politecnica de Catalunya)
DTSTART:20210720T170000Z
DTEND:20210720T180000Z
DTSTAMP:20260423T035019Z
UID:OSGA/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/71/">St
 able solutions to semilinear elliptic equations are smooth up to dimension
  9</a>\nby Xavier Cabre (ICREA and Universitat Politecnica de Catalunya) a
 s part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe regularit
 y of stable solutions to semilinear elliptic PDEs has been studied since t
 he 1970's. In dimensions 10 and higher\, there exist singular stable energ
 y solutions. In this talk I will describe a recent work in collaboration w
 ith Figalli\, Ros-Oton\, and Serra\, where we prove that stable solutions 
 are smooth up to the optimal dimension 9. This answers to an open problem 
 posed by Brezis in the mid-nineties concerning the regularity of extremal 
 solutions to Gelfand-type problems.\n
LOCATION:https://researchseminars.org/talk/OSGA/71/
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