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On some properties of weak solutions to elliptic equations with divergence-free drifts. / Filonov, Nikolay; Shilkin, Timofey.

Contemporary Mathematics. American Mathematical Society, 2018. стр. 105-120 (Contemporary Mathematics; Том 710).

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Harvard

Filonov, N & Shilkin, T 2018, On some properties of weak solutions to elliptic equations with divergence-free drifts. в Contemporary Mathematics. Contemporary Mathematics, Том. 710, American Mathematical Society, стр. 105-120. https://doi.org/10.1090/conm/710/14366

APA

Filonov, N., & Shilkin, T. (2018). On some properties of weak solutions to elliptic equations with divergence-free drifts. в Contemporary Mathematics (стр. 105-120). (Contemporary Mathematics; Том 710). American Mathematical Society. https://doi.org/10.1090/conm/710/14366

Vancouver

Filonov N, Shilkin T. On some properties of weak solutions to elliptic equations with divergence-free drifts. в Contemporary Mathematics. American Mathematical Society. 2018. стр. 105-120. (Contemporary Mathematics). https://doi.org/10.1090/conm/710/14366

Author

Filonov, Nikolay ; Shilkin, Timofey. / On some properties of weak solutions to elliptic equations with divergence-free drifts. Contemporary Mathematics. American Mathematical Society, 2018. стр. 105-120 (Contemporary Mathematics).

BibTeX

@inbook{671e0b27078f4d28b11a5d004241c43d,
title = "On some properties of weak solutions to elliptic equations with divergence-free drifts",
abstract = "We discuss the local properties of weak solutions to the equation −Δu + b · ∇u = 0. The Dirichlet boundary value problem for this equation is studied as well. The corresponding theory is well-known in the case b ∈ Ln, where n is the dimension of the space. Our main interest is focused on the case b ∈ L2. In this case the structure assumption div b = 0 turns out to be crucial.",
keywords = "Elliptic equations, Regularity, Weak solutions",
author = "Nikolay Filonov and Timofey Shilkin",
year = "2018",
month = jan,
day = "1",
doi = "10.1090/conm/710/14366",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "105--120",
booktitle = "Contemporary Mathematics",
address = "United States",

}

RIS

TY - CHAP

T1 - On some properties of weak solutions to elliptic equations with divergence-free drifts

AU - Filonov, Nikolay

AU - Shilkin, Timofey

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We discuss the local properties of weak solutions to the equation −Δu + b · ∇u = 0. The Dirichlet boundary value problem for this equation is studied as well. The corresponding theory is well-known in the case b ∈ Ln, where n is the dimension of the space. Our main interest is focused on the case b ∈ L2. In this case the structure assumption div b = 0 turns out to be crucial.

AB - We discuss the local properties of weak solutions to the equation −Δu + b · ∇u = 0. The Dirichlet boundary value problem for this equation is studied as well. The corresponding theory is well-known in the case b ∈ Ln, where n is the dimension of the space. Our main interest is focused on the case b ∈ L2. In this case the structure assumption div b = 0 turns out to be crucial.

KW - Elliptic equations

KW - Regularity

KW - Weak solutions

UR - http://www.scopus.com/inward/record.url?scp=85050253289&partnerID=8YFLogxK

U2 - 10.1090/conm/710/14366

DO - 10.1090/conm/710/14366

M3 - Chapter

AN - SCOPUS:85050253289

T3 - Contemporary Mathematics

SP - 105

EP - 120

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -

ID: 50940459