Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

Svetlana Mayboroda; Marius Mitrea

doi:10.1007/s10231-004-0125-5

Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

Svetlana Mayboroda, Marius Mitrea

School of Mathematics

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7 Scopus citations

Abstract

We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain Ω, with boundary data in the Besov space B^p,p _s (∂Ω). The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig [14], where the case p > 1 was treated.

Original language	English (US)
Journal	Annali di Matematica Pura ed Applicata
Volume	185
Issue number	2
DOIs	https://doi.org/10.1007/s10231-004-0125-5
State	Published - Jan 1 2006

Keywords

Besov space regularity
Elliptic PDE
Layer potentials
Lipschitz domains
Smoothness

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10.1007/s10231-004-0125-5

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abstract = "We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain Ω, with boundary data in the Besov space Bp,p s (∂Ω). The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig [14], where the case p > 1 was treated.",

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T1 - Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

AU - Mayboroda, Svetlana

AU - Mitrea, Marius

PY - 2006/1/1

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N2 - We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain Ω, with boundary data in the Besov space Bp,p s (∂Ω). The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig [14], where the case p > 1 was treated.

AB - We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain Ω, with boundary data in the Besov space Bp,p s (∂Ω). The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig [14], where the case p > 1 was treated.

KW - Besov space regularity

KW - Elliptic PDE

KW - Layer potentials

KW - Lipschitz domains

KW - Smoothness

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JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 2

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Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

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