Boundary Harnack principle for second order elliptic equations with unbounded drift

H. Kim; M. Safonov

doi:10.1007/s10958-011-0585-2

Boundary Harnack principle for second order elliptic equations with unbounded drift

H. Kim, M. Safonov

Mathematics

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6 Scopus citations

Abstract

We prove the boundary Harnack principle for ratios of solutions u/v 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]. Based on this result, we derive the Hölder regularity of u/v for uniform domains. Bibliography: 27 titles.

Original language	English (US)
Pages (from-to)	127-143
Number of pages	17
Journal	Journal of Mathematical Sciences
Volume	179
Issue number	1
DOIs	https://doi.org/10.1007/s10958-011-0585-2
State	Published - Nov 2011

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title = "Boundary Harnack principle for second order elliptic equations with unbounded drift",

abstract = "We prove the boundary Harnack principle for ratios of solutions u/v 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]. Based on this result, we derive the H{\"o}lder regularity of u/v for uniform domains. Bibliography: 27 titles.",

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AB - We prove the boundary Harnack principle for ratios of solutions u/v 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]. Based on this result, we derive the Hölder regularity of u/v for uniform domains. Bibliography: 27 titles.

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Boundary Harnack principle for second order elliptic equations with unbounded drift

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