Programa de Pós-Graduação em Matemática

The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients

Prof. Boyan Sirakov

Date: 19th February 11:00 am - 11:45 am (UTC -3) Link: PPGM/UFSCar Youtube channel

Abstract: In this joint work with P. Souplet we develop a new, unified approach to the following two classical questions on elliptic PDE: (i) the strong maximum principle for equations with non-Lipschitz nonlinearities; and (ii) 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.