Carleson type estimates for second order elliptic equations with unbounded drift

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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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Second Order Elliptic Equations
Bibliographies
Regularity Conditions
Positive Solution
Bounded Domain
Estimate
Bibliography

Cite this

Carleson type estimates for second order elliptic equations with unbounded drift. / Kim, H.; Safonov, Mikhail V.

In: Journal of Mathematical Sciences, Vol. 176, No. 6, 01.08.2011, p. 928-944.

Research output: Contribution to journalArticle

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