Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift
2011 (English)In: Mathematical Research Letters, ISSN 1073-2780, Vol. 18, no 4, 613-620 p.Article in journal (Refereed) Published
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.
Boundary Point Principle, Strong Maximum Principle, non-divergence form operator, blow-up, singular drift, semi-elliptic operator, pseudo-ball condition, Lyapunov domain, geometric regularity
IdentifiersURN: urn:nbn:se:liu:diva-74436ISI: 000298000100003OAI: oai:DiVA.org:liu-74436DiVA: diva2:484423