Calculus of Variations and Geometric Measure Theory
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Single peak solutions to nonlinear Neumann problems with a degeneracy

Jaeyoung Byeon

created by malchiodi on 14 Nov 2017

20 nov 2017 -- 14:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi

Abstract.

There have been enormous studies on singularly perturbed nonlinear elliptic problems with the Neumann boundary condition. As for a single peak solution which concentrates near a point on the boundary of a given domain, its existence for a critical point of the mean curvature and its nonexistence for the regular point of the mean curvature were known only when a certain nondegeneracy holds. In this talk I would like to explain a purely variational approach to prove the same results without the nondegeneracy.

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