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Weak Harnack's Inequality for non-negative solutions of elliptic equations with potential

Author(s): Ahmed Mohammed
Journal: Proc. Amer. Math. Soc. 129 (2001), 2617-2621.
MSC (2000): Primary 35B05, 35B45, 35D99, 35J10, 35J15
Posted: April 9, 2001
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Abstract | References | Similar articles | Additional information

Abstract:

We present an alternative and shorter proof to a weak Harnack inequality for non-negative solutions of divergence structure elliptic equations with potentials from the Kato class.

References:

1.: F. Chiarenza, E. Fabes, and N. Garofalo, Harnack's inequality for Schrödinger operators and Continuity of solutions, Proc. Amer. Math. Soc. 98 (1986), 415-425. MR 88a:35037
2.: C. E. Gutierrez, Harnack's inequality for degenerate Schrödinger operators, Trans. Amer. Math. Soc. 312 (1989), 403-419. MR 90g:35062
3.: M. Grüter and K.O. Widman, The Green Function for Uniformly Elliptic Equations, Manuscripta Math. 37 (1982), 303-342. MR 83h:35033
4.: K. Kurata, Continuity and Harnack's Inequality for Solutions of Elliptic Partial Differential Equations of Second Order, Indiana Univ. Math. 43 (1994), 411-440. MR 95f:35054


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