Quantization results for higher order Liouville equations
Dr. Ali Hyder,
Johns Hopkins University
| Speaker |
Dr. Ali Hyder,
Johns Hopkins University
|
|---|---|
| When |
Nov 05, 2019
from 04:00 PM to 05:00 PM |
| Where | LH 006 |
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Abstract: I will discuss compactness and blow-up phenomena for the equation \((-\Delta)^m u_k=e^{2mu_k}\) on an open domain in \(\mathbb{R}^{2m}\),
and under the natural integral assumption \(\int_\Omega e^{2mu_k}dx\leq C\). It is well-known that when blow-up occurs, the energy \(\int e^{2mu_k}dx\) is quantized in dimension two,
that is, up to a subsequence, it converges to \(4\pi N\) for some positive integer \(N\). However, in general, the energy is not quantized in dimension four and higher.