Uniqueness of critical points and maximum principles of the singular minimal surface equation |
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Authors: | Rafael López |
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Institution: | Departamento de Geometría y Topología, Instituto de Matemáticas (IEMath-GR), Universidad de Granada, 18071 Granada, Spain |
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Abstract: | We consider a smooth solution of the singular minimal surface equation defined in a bounded strictly convex domain of with constant boundary condition. If , we prove the existence a unique critical point of u. We also derive some and estimates of u by using the theory of maximum principles of Payne and Philippin for a certain family of Φ-functions. Finally we deduce an existence theorem of the Dirichlet problem when . |
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Keywords: | 35B38 35J93 53A10 35J60 Singular minimal surface Critical point Nodal line Maximum principle |
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