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SUMMARY:Seminario Geometría (Virtual): Classification of solutions to the critical p-Laplace equations
DESCRIPTION:Día: 6 de Noviembre de 2020\nHora: 11:30 – 12:30\nLugar: Videoconferencia Sala EUROPA de la UGR\, en Sala EUROPA de la UGR (Acceso Sala Virtual Europa)\nContraseña de la reunión: 237948.\nPonente: Alberto Roncoroni (Universidad de Granada\, España)\n\nResumen:  \nWe consider the following critical p-Laplace equation: \n(1)Δpu+up∗−1=0 in Rn \nwith n≥2 and 1<p<n. Equation (1) has been largely studied in the PDE’s and geometric analysis’ communities\, since extremals of Sobolev inequality solve (1) and\, for p=2\, the equation is related to the Yamabe’s problem. In particular\, it has been recently shown\, exploiting the moving planes method\, that positive solutions to (1) such that \nu∈Lp∗(Rn) and ∇u∈Lp(Rn) \ncan be completely classified. In the talk we will consider the anisotropic critical p-Laplace equation in convex cones of Rn. Since the moving plane method strongly relies on the symmetries of the equation and of the domain\, in the talk a different approach to this problem will be presented. In particular this approach gives a complete classification of the solutions in an anisotropic setting. More precisely\, we characterize solutions to the critical p-Laplace equation induced by a smooth norm inside any convex cone of Rn. \nThis is a joint work with G. Ciraolo and A. Figalli. \nAlba Morquecho Delgado\niemath@ugr.es\nGerencia del Instituto de Matemáticas IEMath-GR
URL:https://canalugr.si2.dev/evento/seminario-geometria-virtual-classification-of-solutions-to-the-critical-p-laplace-equations/
CATEGORIES:Conferencias, seminarios, divulgación científica
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