演講者:黃信元 教授 (國立交通大學應用數學系)
演講者: 黃信元教授 (國立交通大學應用數學系)
標題:Bubbling Solutions for the Liouville systems in a torus
時間:10月07日早上11點00分
地點:校本部第二綜合大樓8樓 B808 教室
摘要: We consider the following Liouville system on a parallelogram Ω in R
2
:where hi(x) ∈ C
3
(Ω), hi(x) > 0, ui
is doubly periodic on ∂Ω(i ∈ I), and A = (aij )n×n is
a non-negative constant matrix. We prove that if
∑
q is a non-degenerate critical point of
n
i=1 ρ
∗
i
log hi(x) and A satisfies certain conditions, (1) has a sequence of fully bubbling
solutions which blow up at p, as ρ = (ρ1, · · · , ρn) → ρ
∗ = (ρ
∗
1
, · · · , ρ∗
n
), where ρ
∗
satisfies
8π
∑n
i=1 ρ
∗
i =
∑n
i=1
∑n
j=1 aijρ
∗
i
ρ
∗
j
and ∑n
i=1 aijρ
∗
i
ρ
∗
j > 6π for j ∈ I.