Self-improving property of the fast diffusion equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10408330" target="_blank" >RIV/00216208:11320/19:10408330 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CMUJuRQEoi" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CMUJuRQEoi</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2019.108291" target="_blank" >10.1016/j.jfa.2019.108291</a>

Result language
angličtina
Original language name
Self-improving property of the fast diffusion equation
Original language description
We show that the gradient of the m-power of a solution to a singular parabolic equation of porous medium-type (also known as fast diffusion equation), satisfies a reverse Holder inequality in suitable intrinsic cylinders. Relying on an intrinsic Calderon-Zygmund covering argument, we are able to prove the local higher integrability of such a gradient for m is an element of ((n-2)(+)/n+2, 1). Our estimates are satisfied for a general class of growth assumptions on the non linearity. In this way, we extend the theory for m >= 1 (see [16] in the list of references) to the singular case. In particular, an intrinsic metric that depends on the solution itself is introduced for the singular regime. (C) 2019 Elsevier Inc. All rights reserved.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)