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

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

Bibliographical note

Funding Information:
We would like to thank the American Institute of Mathematics for hosting the SQuaRE workshop on “Singular integral operators and solvability of boundary problems for elliptic equations with rough coefficients,” at which many of the results and techniques of this paper were discussed. Steve Hofmann is partially supported by the NSF grant DMS-1361701. Svitlana Mayboroda is partially supported by the Alfred P. Sloan Fellowship, the NSF CAREER Award DMS 1056004, the NSF INSPIRE Award DMS 1344235, and the NSF Materials Research Science and Engineering Center Seed Grant.

Funding Information:
Acknowledgements We would like to thank the American Institute of Mathematics for hosting the SQuaRE workshop on “Singular integral operators and solvability of boundary problems for elliptic equations with rough coefficients,” at which many of the results and techniques of this paper were discussed. Steve Hofmann is partially supported by the NSF grant DMS-1361701. Svitlana Mayboroda is partially supported by the Alfred P. Sloan Fellowship, the NSF CAREER Award DMS 1056004, the NSF INSPIRE Award DMS 1344235, and the NSF Materials Research Science and Engineering Center Seed Grant.

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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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.",

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

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