Boundary Harnack principle for second order elliptic equations with unbounded drift

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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 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 languageEnglish (US)
Pages (from-to)127-143
Number of pages17
JournalJournal of Mathematical Sciences
Volume179
Issue number1
DOIs
StatePublished - Nov 1 2011

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