Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation
| dc.creator | Bonforte, M. | |
| dc.creator | Iagar, R. G. | |
| dc.creator | Vazquez, J. L. | |
| dc.date | 2009-02-16 | |
| dc.date.accessioned | 2026-07-07T12:42:18Z | |
| dc.date.available | 2026-07-07T12:42:18Z | |
| dc.description | We study qualitative and quantitative properties of local weak solutions of the fast $p$-Laplacian equation, $\partial_t u=Δ_{p}u$, with $1<p<2$. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of $\RR^n\times [0,T]$. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion range, that is when $1<p \le 2n/(n+1)$. The boundedness results may be also extended to the limit case $p=1$, while the positivity estimates cannot. We prove the existence as well as sharp asymptotic estimates for the so-called large solutions for any $1<p<2$, and point out their main properties. We also prove a new local energy inequality for suitable norms of the gradients of the solutions. As a consequence, we prove that bounded local weak solutions are indeed local strong solutions, more precisely $\partial_t u\in L^2_{\rm loc}$. | |
| dc.identifier | https://arxiv.org/abs/0902.2750 | |
| dc.identifier | http://arxiv.org/abs/0902.2750 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220033 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B35; 35B65; 35K55; 35K65 | |
| dc.title | Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation | |
| dc.type | text |