Poincaré-Perron's method for the Dirichlet problem on stratified sets |
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| Authors: | Serge Nicaise Oleg M Penkin |
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| Institution: | a Institut des Sciences et Techniques de Valenciennes, MACS, Université de Valenciennes et du Hainaut Cambrésis, 59313 Valenciennes Cedex 9, France
b Voronezh State University, Universitetskaja pl. 1, 394000 Voronezh, Russia |
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| Abstract: | We extend standard Poincaré-Perron's method to the Dirichlet problem on a class of multistructures. This method is based on the spherical mean theorem, the construction of fundamental solutions and on Harnack's inequality on such domains, that we first establish. |
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| Keywords: | Perron's method Harnack's inequality Multistructures |
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