Carleson type estimates for second order elliptic equations with unbounded drift

H. Kim, M. Safonov

Research output: Contribution to journalArticle

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Abstract

We derive a Carleson type estimate for positive solutions of non-divergence second order elliptic equations Lu = aijDiju + biDiu = 0 in a bounded domain Ω ⊂ Rn. We assume that bi ∈ Ln(Ω) and Ω is a twisted Hölder domain of order α ∈ (1/2, 1] which satisfies a weak regularity condition. We also provide an example which shows that the main result fails in general if α ∈ (0, 1/2]. Bibliography: 18 titles.

Original languageEnglish (US)
Pages (from-to)928-944
Number of pages17
JournalJournal of Mathematical Sciences
Volume176
Issue number6
DOIs
StatePublished - Aug 1 2011

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