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2004 Square-function estimates for singular integrals and applications to partial differential equations
Svitlana Mayboroda, Marius Mitrea
Differential Integral Equations 17(7-8): 873-892 (2004).

Abstract

The purpose of the present paper is to continue the program of study of elliptic boundary-value problems on Lipschitz domains with boundary data in quasi-Banach Besov spaces $B_s^{p,p}(\partial \Omega)$, initiated in [13]. Introducing a modified square function which is well-adapted for handling data with a fractional amount of smoothness, we establish the well-posedness of the Dirichlet and Neumann boundary problems for the Laplacian in Lipschitz domains, for a range of indices which includes values of $p$ less than $1$. An important ingredient in this regard is establishing suitable square-function estimates for a singular integral of potential type.

Citation

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Svitlana Mayboroda. Marius Mitrea. "Square-function estimates for singular integrals and applications to partial differential equations." Differential Integral Equations 17 (7-8) 873 - 892, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.35375
MathSciNet: MR2075411

Subjects:
Primary: 35J25
Secondary: 31B10 , 42B20 , 46E35

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 7-8 • 2004
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