Local behavior for solutions to anisotropic weighted quasilinear degenerate parabolic equations

Autor:	Miao, Changxing, Zhao, Zhiwen
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the asymptotic behavior of the solution near the singular or degenerate point of the weights. In particular, we find an explicit upper bound on the decay rate exponent determined by the structures of the equations and weights, which can be achieved under certain condition and meanwhile reflects the damage effect of the weights on the regularity of the solution. Furthermore, we prove the local H\"{o}lder regularity of solutions to non-homogeneous parabolic $p$-Laplace equations with single power-type weights. Comment: We present a more concise and elegant proof by combining intrinsic scaling technique and exponential variable substitution
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.20622 Zobrazit plný text záznamu View this record from Arxiv