Seminari del Dipartimento


Analisi Matematica

Singular limits for a half-Laplacian Liouville type equation

Antonio J. Fernandez

18-05-2022 - 14:30
Largo San Leonardo Murialdo,1 - Pal.C _Aula 211


We consider the nonlocal Liouville type equation
(-Delta)^(1/2)u = epsilon * k(x) e^u, u > 0 in I
u = 0 in R I
where I is a union of d >= 2 disjoint bounded intervals, k is a smooth bounded function with positive infimum and epsilon > 0 is a small parameter. For any integer 1 <= m <= d, we construct a family of solution u_epsilon which blow-up at m distinct points of I and for which epsilon *(integral of k(x) e^u) --> 2m*pi as epsilon --> 0$. Moreover, we show that, when d = 2 and m is suitably large, no such construction is possible. The talk is based on a joint work with Matteo Cozzi (Milano, Italy).

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