Por Boyan Sirakov (PUC - Rio).
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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The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.
