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SUMMARY:Andrea Malchiodi (Scuola Normale Superiore)
DTSTART:20210420T170000Z
DTEND:20210420T180000Z
DTSTAMP:20260423T035057Z
UID:OSGA/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/57/">On
  critical points of the Moser-Trudinger functional</a>\nby Andrea Malchiod
 i (Scuola Normale Superiore) as part of Online Seminar "Geometric Analysis
 "\n\n\nAbstract\nIt is known that in two dimensions Sobolev functions in $
 W^{1\,2}$ satisfy critical embedding properties of exponential type. In 19
 71 Moser obtained a sharp form of the embedding\, controlling the integrab
 ility of $F(u) := \\int \\exp(u^2)$ in terms of the Sobolev norm of $u$.\n
 On a closed Riemannian surface\, $F(u)$ is unbounded above for $\\|u\\|_{W
 ^{1\,2}} > 4 \\pi$. \nWe are however able to find critical points of $F$ c
 onstrained to any sphere \n$\\{ \\|u\\|_{W^{1\,2}} = \\beta \\}$\, with $\
 \beta > 0$ arbitrary. The proof combines min-max theory\, a monotonicity a
 rgument by Struwe\, blow-up analysis and compactness estimates. This is jo
 int work with F. De Marchis\, O. Druet\, L. Martinazzi and P. D. Thizy.\n
LOCATION:https://researchseminars.org/talk/OSGA/57/
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