Square function estimates on layer potentials for higher-order elliptic equations

Ariel Barton; Steve Hofmann; Svitlana Mayboroda

doi:10.1002/mana.201600116

Square function estimates on layer potentials for higher-order elliptic equations

Ariel Barton, Steve Hofmann, Svitlana Mayboroda

School of Mathematics

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

9 Scopus citations

Abstract

In this paper we establish square-function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This generalizes known results for variable-coefficient second-order operators, and also for constant-coefficient higher-order operators.

Original language	English (US)
Pages (from-to)	2459-2511
Number of pages	53
Journal	Mathematische Nachrichten
Volume	290
Issue number	16
DOIs	https://doi.org/10.1002/mana.201600116
State	Published - Nov 2017

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Publisher Copyright:
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Keywords

35C15
Elliptic equation
Primary: 35J30; Secondary: 31B10
higher-order differential equation
layer potentials
square function estimates

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10.1002/mana.201600116

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abstract = "In this paper we establish square-function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This generalizes known results for variable-coefficient second-order operators, and also for constant-coefficient higher-order operators.",

keywords = "35C15, Elliptic equation, Primary: 35J30; Secondary: 31B10, higher-order differential equation, layer potentials, square function estimates",

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T1 - Square function estimates on layer potentials for higher-order elliptic equations

AU - Barton, Ariel

AU - Hofmann, Steve

AU - Mayboroda, Svitlana

PY - 2017/11

Y1 - 2017/11

N2 - In this paper we establish square-function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This generalizes known results for variable-coefficient second-order operators, and also for constant-coefficient higher-order operators.

AB - In this paper we establish square-function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This generalizes known results for variable-coefficient second-order operators, and also for constant-coefficient higher-order operators.

KW - 35C15

KW - Elliptic equation

KW - Primary: 35J30; Secondary: 31B10

KW - higher-order differential equation

KW - layer potentials

KW - square function estimates

UR - https://www.scopus.com/pages/publications/85016413856

UR - https://www.scopus.com/inward/citedby.url?scp=85016413856&partnerID=8YFLogxK

U2 - 10.1002/mana.201600116

DO - 10.1002/mana.201600116

M3 - Article

AN - SCOPUS:85016413856

SN - 0025-584X

VL - 290

SP - 2459

EP - 2511

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 16

ER -

Square function estimates on layer potentials for higher-order elliptic equations

Abstract

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