Abstract
This is a report on some recent results obtained by the authors on unique continuation at boundary points for harmonic functions satisfying appropriate local sign conditions on the boundary. The authors’ investigation was initially motivated by some questions in several complex variables. After we present the main results we shall indicate the connection to these questions. We will also mention some open related problems. We consider an open set Ω in ℝn and a boundary point x 0. We need to assume that, near x 0, the boundary of Ω is either a piece of a hyperplane or a piece of a sphere. We state our results in the latter case.KeywordsHarmonic FunctionBoundary PointOpen NeighborhoodFinite TypeReal HypersurfaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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