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Lisbon WADE — Webinar em Análise e Equações Diferenciais   RSS

Boyan Sirakov 25/02/2021, 14:00 — 15:00 — Online
, PUC - Rio

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

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.

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Iniciativa conjunta dos centros de investigação CAMGSD, CMAFcIO and GFM.

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