Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 545-565

CAUCHY INTEGRALS FOR THE p-LAPLACE EQUATION IN PLANAR LIPSCHITZ DOMAINS

Kaj Nyström and Andreas Rosén

Uppsala University, Department of Mathematics
S-751 06 Uppsala, Sweden; kaj.nystrom 'at' math.uu.se

Chalmers University of Technology and University of Gothenburg, Mathematical Sciences
S-412 96 Göteborg, Sweden; andreas.rosen 'at' chalmers.se

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.

2010 Mathematics Subject Classification: Primary 35J92, 47A60; Secondary 35J62, 35J70.

Key words: p-Laplace, p-harmonic, quasi-linear, Cauchy integral, functional calculus.

Reference to this article: K. Nyström and A. Rosén: Cauchy integrals for the p-Laplace equation in planar Lipschitz domains. Ann. Acad. Sci. Fenn. Math. 39 (2014), 545-565.

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doi:10.5186/aasfm.2014.3939