The Averaging lemma and regularizing effect
| dc.creator | Tadmor, Eitan | |
| dc.creator | Tao, Terence | |
| dc.date | 2005-11-02 | |
| dc.date.accessioned | 2026-07-07T06:50:41Z | |
| dc.date.available | 2026-07-07T06:50:41Z | |
| dc.description | We prove new velocity averaging results for second-order multidimensional equations of the general form, $\op(\nabla_x,v)f(x,v)=g(x,v)$ where $\op(\nabla_x,v):=\bba(v)\cdot\nabla_x-\nabla_x^\top\cdot\bbb(v)\nabla_x$. These results quantify the Sobolev regularity of the averages, $\int_vf(x,v)ϕ(v)dv$, in terms of the non-degeneracy of the set $\{v: |\op(\ixi,v)|\leq δ\}$ and the mere integrability of the data, $(f,g)\in (L^p_{x,v},L^q_{x,v})$. Velocity averaging is then used to study the \emph{regularizing effect} in quasilinear second-order equations, $\op(\nabla_x,ρ)ρ=S(ρ)$ using their underlying kinetic formulations, $\op(\nabla_x,v)χ_ρ=g_{{}_S}$. In particular, we improve previous regularity statements for nonlinear conservation laws, and we derive completely new regularity results for convection-diffusion and elliptic equations driven by degenerate, non-isotropic diffusion. | |
| dc.description | 28 pages; no figures; submitted, Comm. Pure. Appl. Math | |
| dc.identifier | https://arxiv.org/abs/math/0511054 | |
| dc.identifier | http://arxiv.org/abs/math/0511054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104740 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L65; 35K57 | |
| dc.title | The Averaging lemma and regularizing effect | |
| dc.type | text |