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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

19 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

Bibliographical note

Publisher Copyright:
© 2021 American Mathematical Society

Publisher link

10.1090/tran/8282

Find It

Find It at U of M Libraries

Cite this

@article{6d018db4155f48c8b87be4d7e11d2aef,

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

abstract = "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.",

author = "Krylov, \{N. V.\}",

note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society",

year = "2021",

month = apr,

doi = "10.1090/tran/8282",

language = "English (US)",

volume = "374",

pages = "2805--2822",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - Elliptic equations with VMO a, b ∈ Ld, and C ∈ Ld/2

AU - Krylov, N. V.

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85102107303

UR - https://www.scopus.com/inward/citedby.url?scp=85102107303&partnerID=8YFLogxK

U2 - 10.1090/tran/8282

DO - 10.1090/tran/8282

M3 - Article

AN - SCOPUS:85102107303

SN - 0002-9947

VL - 374

SP - 2805

EP - 2822

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 4

ER -