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Narrow Domains and the Harnack Inequality for Elliptic Equations


Author: M. V. Safonov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 509-522
MSC (2010): Primary 35J15; Secondary 35B45, 35B65
Published electronically: March 30, 2016
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Abstract: We present a direct proof of Moser's Harnack inequality that does not involve iterations. The method is based on a recursive estimate for solutions in domains of small measure. Such estimates can also be useful for other applications.


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Additional Information

M. V. Safonov
Affiliation: School of Mathematics, University of Minnesota
Email: safonov@math.umn.edu

DOI: https://doi.org/10.1090/spmj/1401
Keywords: Second-order elliptic equations, Harnack inequality, measurable coefficients
Received by editor(s): February 19, 2015
Published electronically: March 30, 2016
Dedicated: Dedicated to Nina N. Ural’tseva
Article copyright: © Copyright 2016 American Mathematical Society