Calculus of Variations and Geometric Measure Theory
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Critical points and extremals of the Moser-Trudinger inequality in two dimension

Luca Martinazzi (University of Padua)

created by malchiodi on 13 Feb 2017

16 feb 2017 -- 17:00   [open in google calendar]

Scuola Normale Superiore, Aula Tonelli

Abstract.

We shall give a new approach to the Moser-Trudinger inequality (a critical version of the Sobolev inequality) and the existence of extremals on the unit disk in the plane. Subtly estimating the energy of critical points of subcritical Moser-Trudinger inequalities, we will show that a suitable sequence of such critical points does not blow up and in fact converges to an extremal of the critical Moser-Trudinger inequality. Several open questions will be discussed. This is a joint work with Gabriele Mancini and builds upon a previous work joint with Andrea Malchiodi.

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