On the solvability of a boundary-value problem for an elliptic equation |
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Authors: | A. M. Il’in S. V. Rep’evskii |
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Affiliation: | 1. Chelyabinsk State University, Chelyabinsk, Russia
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Abstract: | Consider a boundary-value problem for a second-order linear elliptic equation in a bounded domain. The coefficient of the required function is nonpositive everywhere in the domain, except for a small neighborhood of an interior point. The following question arises: Under what constraints on this coefficient in the given small domain do the statements on the existence and uniqueness of the solution of the first boundary-value problem remain valid? |
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