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

N. V. Krylov

doi:10.1090/tran/8282

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

N. V. Krylov

Mathematics

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11 Scopus citations

Abstract

We consider elliptic equations with operators L = a^ijD_ij+bⁱD_i−c with a being almost in VMO, b ∈ L_d and c ∈ L_q, c ≥ 0, d > q ≥ d/2. We prove the solvability of Lu = f ∈ L_p in bounded C^1,1-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 language	English (US)
Pages (from-to)	2805-2822
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	4
DOIs	https://doi.org/10.1090/tran/8282
State	Published - Apr 2021

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© 2021 American Mathematical Society

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