Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations
| dc.creator | Bonforte, Matteo | |
| dc.creator | Vazquez, Juan Luis | |
| dc.date | 2008-05-30 | |
| dc.date | 2008-12-01 | |
| dc.date.accessioned | 2026-07-07T12:05:51Z | |
| dc.date.available | 2026-07-07T12:05:51Z | |
| dc.description | We investigate qualitative properties of local solutions $u(t,x)\ge 0$ to the fast diffusion equation, $\partial_t u =Δ(u^m)/m$ with $m<1$, corresponding to general nonnegative initial data. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of the form $[0,T]\times\RR^d$. They combine into forms of new Harnack inequalities that are typical of fast diffusion equations. Such results are new for low $m$ in the so-called very fast diffusion range, precisely for all $m\le m_c=(d-2)/d.$ The boundedness statements are true even for $m\le 0$, while the positivity ones cannot be true in that range. | |
| dc.description | 36 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0805.4823 | |
| dc.identifier | http://arxiv.org/abs/0805.4823 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208488 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B45, 35B65, 35K55, 35K65 | |
| dc.title | Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations | |
| dc.type | text |