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Boundary trace of the solutions of the prescribed Gaussian curvature equation

Published online by Cambridge University Press:  11 July 2007

Michele Grillot  and
Laurent Véron
Michele Grillot
Affiliation:
Laboratoire de Mathématiques et Physique Mathématique, CNRS UMR 6628, Faculté des Sciences, B.P. 6759, 45067 Orléans cedex 2, France
Laurent Véron
Affiliation:
Laboratoire de Mathématiques et Physique Théorique, CNRS UPRES-A 6083, Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France
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Abstract

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We study the existence of a boundary trace for minorized solutions of the equation Δu + K (x) e2u = 0 in the unit open ball B2 of R2. We prove that this trace is an outer regular Borel measure on ∂B2, not necessarily a Radon measure. We give sufficient conditions on Borel measures on ∂B2 so that they are the boundary trace of a solution of the above equation. We also give boundary removability results in terms of generalized Bessel capacities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 3 , June 2000 , pp. 527 - 560
Copyright
Copyright © Royal Society of Edinburgh 2000