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

DOI:
https://doi.org/10.1090/S0002-9939-1986-0857933-4

MathSciNet review:
857933

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a uniform Harnack inequality for nonnegative solutions of , where is a second order elliptic operator in divergence form, and 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 .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0857933-4

Keywords:
Harnack's inequality,
Schrödinger equation

Article copyright:
© Copyright 1986
American Mathematical Society