On the isomorphic mapping of weighted spaces by an elliptic operator with degeneration on the domain boundary |
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Authors: | V A Rukavishnikov E I Rukavishnikova |
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Institution: | 1. Computer Center, Far-Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia
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Abstract: | We consider the first boundary value problem for a second-order elliptic equation with degeneration on the entire twice continuously differentiable boundary of a two-dimensional domain Ω; this problem has a generalized solution in the weighted space . We find conditions ensuring that the generalized solution belongs to the narrower space , which permits obtaining estimates for the convergence rate of an approximate finite-element solution to the exact solution in the norms of the spaces and L 2(Ω). |
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