The V\'azquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients

Autor:	Sirakov, Boyan, Souplet, Philippe
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	We develop a new, unified approach to the following two classical questions on elliptic PDE: the strong maximum principle for equations with non-Lipschitz nonlinearities, and the at most exponential decay of solutions in the whole space or exterior domains. Our results apply to divergence and nondivergence operators with locally unbounded lower-order coefficients, in a number of situations where all previous results required bounded ingredients. Our approach, which allows for relatively simple and short proofs, is based on a (weak) Harnack inequality with optimal dependence of the constants in the lower-order terms of the equation and the size of the domain, which we establish. Comment: 21 pages, accepted version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.08511 Zobrazit plný text záznamu View this record from Arxiv