2000 character limit reached
Divergent operator with degeneracy and related sharp inequalities (1910.13924v5)
Published 30 Oct 2019 in math.AP
Abstract: In this paper we classify all positive extremal functions to a sharp weighted Sobolev inequality on the upper half space, which involves divergent operators with degeneracy on the boundary. As an application of the results, we can derive a sharp Sobolev type inequality involving Baouendi-Grushin operator, and classify certain extremal functions for all $\tau>0$ and $m\ne2 $ or $ n\ne1$.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.