Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Harnack's inequality for Schrödinger operators and the continuity of solutions

Authors: F. Chiarenza, E. Fabes and N. Garofalo
Journal: Proc. Amer. Math. Soc. 98 (1986), 415-425
MSC: Primary 35B99; Secondary 35D10, 35J15
MathSciNet review: 857933
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Abstract: We prove a uniform Harnack inequality for nonnegative solutions of $ Au = Vu$, where $ A$ is a second order elliptic operator in divergence form, and $ V$ belongs to the Stummel class of potentials. As a consequence we obtain the continuity of a general weak solution. These results extend the previous work of Aizenman and Simon for $ \Delta u = Vu$.

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Keywords: Harnack's inequality, Schrödinger equation
Article copyright: © Copyright 1986 American Mathematical Society