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Cauchy integrals for the p-Laplace equation in planar Lipschitz domains

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Author(s): Kaj Nyström , Andreas Rosén

Publication date Created: 27 May 2013

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Abstract

We construct solutions to p-Laplace type equations in unbounded Lipschitz domains in the plane with prescribed boundary data in appropriate fractional Sobolev spaces. Our approach builds on a Cauchy integral representation formula for solutions.

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Most cited references 6

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Quadratic estimates and functional calculi of perturbed Dirac operators

, , (2005)

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on compact manifolds depend analytically on \(L_\infty\) changes in the metric. We also recover a unified proof of many results in the Calder\'on program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.

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Cauchy integrals on Lipschitz curves and related operators

A. P. Calderon (1977)

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Weighted maximal regularity estimates and solvability of nonsmooth elliptic systems II

Pascal Auscher, Andreas Rosén, A. Rösen-Wolv (2012)

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Publication date Created: 27 May 2013

Publication date Updated: 2014-02-27

Article

ArXiV ID: 1305.6152

SO-VID: c34c023e-a1a6-44d6-89f9-c74c65af1a40

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Comments Error in proof corrected

Categories math.AP

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