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Information Center for Mathematical Science

PAC

The Harnack inequality for second-order elliptic equations with divergence-free drifts
Author Lenya Ryzhik (Stanford University)
Homepage Url http://math.stanford.edu/~ryzhik/
Coauthors Mihaela Ignatova, Igor Kukavica
Abstract We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b 2 Ln=2+ \L2 where  > 0. As an application we provide a one sided Liouville's theorem provided that b 2 Ln=2+(Rn) \ L2(Rn).
Abstract Url http://math.stanford.edu/~ryzhik/ikr-submit.pdf