UNAM

CONCENTRATING SOLUTIONS FOR A BIHARMONIC PROBLEM

Ponente: Jorge Faya
Institución: Universidad Austral de Chile
 Tipo de Evento: Investigación
Cuándo 17/10/2024
de 10:30 a 11:30
Dónde Seminario online
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Consider the problem:

∆(a∆u) = a |u|^(p−2−ε)u = 0 in Ω,

u=0 on ∂Ω, ∆u=0  on ∂Ω,

where Ω is a smooth bounded domain in RN with N ≥ 5 . Here, the exponent p := 2N/N-4 is Sobolev critical exponent for the embedding H2 ∩H1(Ω) → Lp(Ω) and  a is a C2-class function which is strictly positive in Ω.

In this talk we present conditions on the function a and the domain Ω that are sufficient for the problem to admit positive and sign-changing solutions, with an explicit asymptotic profile, which concentrate and blow up at a point on the boundary ∂Ω as ε tends to 0

This is joint work with professors Salomón Alarcón and Carolina Rey.