A fractional Yamabe flow and some applications
By Tianling Jin, Jingang Xiong. 2011
71 citations recorded by the source corpus.
We introduce a fractional Yamabe flow involving nonlocal conformally invariant operators on the conformal infinity of asymptotically hyperbolic manifolds, and show that on the conformal spheres $(\Sn, [g_{\Sn}])$, it converges to the standard sphere up to a M\"obius diffeomorphism. This result allows us to obtain extinction profiles of solutions of some fractional porous medium equations. In the end, we use this fractional fast diffusion equation, together with its extinction profile and some estimates of its extinction time, to improve a Sobolev inequality via a quantitative estimate of the remainder term.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/4a2d88eaed7fe1eed2b167d7bf7c081f7cecce5f
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In Applied Mathematics
- Rupert L. Frank
- Shibing Chen
- Tobias Weth
- Jean Van Schaftingen
- X. Tang
- M. Fall
- Mihai Marics
- Bartłomiej Dyda
In Computational Theory and Mathematics
- Rupert L. Frank
- Shibing Chen
- Tobias Weth
- Jean Van Schaftingen
- X. Tang
- Mihai Marics
- Wei Shuai
- M. Fall
Citations in the corpus
- Remainder terms in the fractional Sobolev inequality (2012, background): “, [10, 11, 17]); see also [7] for a recent application of remainder terms.”