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arXiv · 2010.08511

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

Boyan Sirakov·Philippe Souplet
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Abstract

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.

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Boyan Sirakov, Philippe Souplet. 2020-10-16. The V\'azquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients. https://arxiv.org/abs/2010.08511

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