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# Quantization results for higher order Liouville equations

Dr. Ali Hyder, Johns Hopkins University
 Speaker Dr. Ali Hyder, Johns Hopkins University Nov 05, 2019 from 04:00 PM to 05:00 PM LH 006 vCal iCal

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.

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