Elliptic equations with VMO a, b ∈ Ld, and C ∈ Ld/2

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We consider elliptic equations with operators L = aijDij+biDi−c with a being almost in VMO, b ∈ Ld and c ∈ Lq, c ≥ 0, d > q ≥ d/2. We prove the solvability of Lu = f ∈ Lp in bounded C1,1-domains, 1 < p ≤ q, and of λu−Lu = f in the whole space for any λ > 0. Weak uniqueness of the martingale problem associated with such operators is also obtained.

Original languageEnglish (US)
Pages (from-to)2805-2822
Number of pages18
JournalTransactions of the American Mathematical Society
Issue number4
StatePublished - Apr 2021

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