Boundary trace of the solutions of the prescribed Gaussian curvature equation
Michèle Grillot, Лаурент Верон · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2000
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.