Calculus of Variations and Geometric Measure Theory
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Singular solutions, minimal cones and the Hsiang problem

Vladimir Tkachev

created by malchiodi on 13 Feb 2017

16 feb 2017 -- 16:00   [open in google calendar]

Scuola Normale Superiore, Aula Tonelli

Abstract.

Minimal cones arise as singular solutions of the 1-Laplace equation and played a crucial role in both the solution of the famous Bernstein problem and in the construction of the higher dimensional counterexamples by Bombieri, de Giorgi and Giusti. Quadratic minimal cones were completely classified by Hsiang in the late `60s. Cubic minimal cones have been the subject of considerable recent interest, but there is still very little known about their structure. On the other hand, cubic minimal cones have recently appeared in the context of singular and truly viscosity solutions to fully nonlinear uniformly elliptic PDEs. An unexpected unifying tool behind these problems is a novel nonassociative algebras approach. In my talk, I will explain how these different topics comes into play. A part of the talk is based on a joint work with N. Nadirashvili och S.Vladut (CNRS et Université d'Aix-Marseille).

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