Carleson type estimates for second order elliptic equations with unbounded drift

H. Kim; M. Safonov

doi:10.1007/s10958-011-0444-1

Carleson type estimates for second order elliptic equations with unbounded drift

H. Kim, M. Safonov

Mathematics

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4 Scopus citations

Abstract

We derive a Carleson type estimate for positive solutions of non-divergence second order elliptic equations Lu = a_ijD_iju + b_iD_iu = 0 in a bounded domain Ω ⊂ Rⁿ. We assume that b_i ∈ 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 language	English (US)
Pages (from-to)	928-944
Number of pages	17
Journal	Journal of Mathematical Sciences
Volume	176
Issue number	6
DOIs	https://doi.org/10.1007/s10958-011-0444-1
State	Published - Aug 2011

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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 H{\"o}lder 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.",

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AU - Safonov, M.

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AB - 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.

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Carleson type estimates for second order elliptic equations with unbounded drift

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