Boundary trace of the solutions of the prescribed Gaussian curvature equation
Published online by Cambridge University Press: 11 July 2007
Abstract
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
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