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Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift
University of Missouri.
University of Missouri.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
University of Missouri.
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2011 (English)In: Mathematical Research Letters, ISSN 1073-2780, Vol. 18, no 4, 613-620 p.Article in journal (Refereed) Published
Abstract [en]

We discuss a sharp generalization of the Hopf-Oleinik boundary point principle (BPP) for domains satisfying an interior pseudo-ball condition, for non-divergence form, semi-elliptic operators with singular drift. In turn, this result is used to derive a version of the strong maximum principle under optimal pointwise blow-up conditions for the coefficients of the differential operator involved. We also explain how a uniform two-sided pseudo-ball condition may be used to provide a purely geometric characterization of Lyapunov domains, and clarify the role this class of domains plays vis-a-vis to the BPP.

Place, publisher, year, edition, pages
International Press , 2011. Vol. 18, no 4, 613-620 p.
Keyword [en]
Boundary Point Principle, Strong Maximum Principle, non-divergence form operator, blow-up, singular drift, semi-elliptic operator, pseudo-ball condition, Lyapunov domain, geometric regularity
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-74436ISI: 000298000100003OAI: diva2:484423
Available from: 2012-01-27 Created: 2012-01-27 Last updated: 2012-02-06

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Maz´ya, Vladimir
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