| Abstract: |
| In this talk, I will report our recent results on the stability of the Caffarelli-Kohn-Nirenberg inequality both in the functional inequality setting and in the critical point setting. In these results, we establish the sharp Bianchi-Egnell stability in the functional inequality setting under the nondegenerate assumption and discuss the existence of minimizers of the variational problem related to the optimal constant. We also establish the sharp Figalli-Glaudo stability in the critical point setting both under the nondegenerate assumption and the degenerate assumption. Rather surprisingly, the optimal power of the stability under the degenerate assumption is an absolute constant which is independent of the power of the nonlinearity and the number of bubbles. |
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