Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications

Autor:	Koike, Shigeaki, Swiech, Andrzej, Tateyama, Shota
Rok vydání:	2018
Předmět:	Mathematics - Analysis of PDEs 49L25 35D40 35B65 35K55 35K20 35K10
Druh dokumentu:	Working Paper
Popis:	The weak Harnack inequality for $L^p$-viscosity supersolutions of fully nonlinear second-order uniformly parabolic partial differential equations with unbounded coefficients and inhomogeneous terms is proved. It is shown that H\"older continuity of $L^p$-viscosity solutions is derived from the weak Harnack inequality for $L^p$-viscosity supersolutions. The local maximum principle for $L^p$-viscosity subsolutions and the Harnack inequality for $L^p$-viscosity solutions are also obtained. Several further remarks are presented when equations have superlinear growth in the first space derivatives. Comment: 33 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.07510 Zobrazit plný text záznamu View this record from Arxiv