A review of some new results in the theory of linear elliptic equations with drift in Ld

N. V. Krylov

doi:10.1007/s13324-021-00508-1

A review of some new results in the theory of linear elliptic equations with drift in L_d

N. V. Krylov

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

1 Scopus citations

Abstract

We present an overview of recent results of the author related to the Aleksandrov type estimates with power of summability of the free term d< d, the Harnack inequality for u∈Wd0,loc2, Hölder continuity of L-harmonic and L-caloric functions. Under the assumption that the main coefficients are almost in VMO (and b∈ L_d) we also present the results about solvability of the elliptic equations in Wd02 in domains and in the whole space. A few relates issues are discussed as well.

Original language	English (US)
Article number	73
Journal	Analysis and Mathematical Physics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s13324-021-00508-1
State	Published - Jun 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Second-order equations
Semigroups
Singular coefficients
Vanishing mean oscillation

Access

10.1007/s13324-021-00508-1

OpenUrl availability

Full text

Cite this

@article{e970ebc08ca447f29a9d91e8f9195486,

title = "A review of some new results in the theory of linear elliptic equations with drift in Ld",

abstract = "We present an overview of recent results of the author related to the Aleksandrov type estimates with power of summability of the free term d< d, the Harnack inequality for u∈Wd0,loc2, H{\"o}lder continuity of L-harmonic and L-caloric functions. Under the assumption that the main coefficients are almost in VMO (and b∈ Ld) we also present the results about solvability of the elliptic equations in Wd02 in domains and in the whole space. A few relates issues are discussed as well.",

keywords = "Second-order equations, Semigroups, Singular coefficients, Vanishing mean oscillation",

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

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = jun,

doi = "10.1007/s13324-021-00508-1",

language = "English (US)",

volume = "11",

journal = "Analysis and Mathematical Physics",

issn = "1664-2368",

publisher = "Springer Science + Business Media",

number = "2",

}

TY - JOUR

T1 - A review of some new results in the theory of linear elliptic equations with drift in Ld

AU - Krylov, N. V.

PY - 2021/6

Y1 - 2021/6

N2 - We present an overview of recent results of the author related to the Aleksandrov type estimates with power of summability of the free term d< d, the Harnack inequality for u∈Wd0,loc2, Hölder continuity of L-harmonic and L-caloric functions. Under the assumption that the main coefficients are almost in VMO (and b∈ Ld) we also present the results about solvability of the elliptic equations in Wd02 in domains and in the whole space. A few relates issues are discussed as well.

AB - We present an overview of recent results of the author related to the Aleksandrov type estimates with power of summability of the free term d< d, the Harnack inequality for u∈Wd0,loc2, Hölder continuity of L-harmonic and L-caloric functions. Under the assumption that the main coefficients are almost in VMO (and b∈ Ld) we also present the results about solvability of the elliptic equations in Wd02 in domains and in the whole space. A few relates issues are discussed as well.

KW - Second-order equations

KW - Semigroups

KW - Singular coefficients

KW - Vanishing mean oscillation

UR - http://www.scopus.com/inward/record.url?scp=85102203504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85102203504&partnerID=8YFLogxK

U2 - 10.1007/s13324-021-00508-1

DO - 10.1007/s13324-021-00508-1

M3 - Article

AN - SCOPUS:85102203504

SN - 1664-2368

VL - 11

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 2

M1 - 73

ER -