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.
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Dedicated to the memory of Pierre Grisvard
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© 1996 Birkhäuser Boston
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Baouendi, M.S., Rothschild, L.P. (1996). Unique Continuation of Harmonic Functions at Boundary Points and Applications to Problems in Complex Analysis. In: Cea, J., Chenais, D., Geymonat, G., Lions, J.L. (eds) Partial Differential Equations and Functional Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 22. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2436-5_3
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DOI: https://doi.org/10.1007/978-1-4612-2436-5_3
Publisher Name: Birkhäuser Boston
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