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On the Solvability of a Boundary-Value Problem for an Elliptic Equation
A. M. Il'in, S. V. Repjevskij Chelyabinsk State University
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?
Keywords:
second-order linear elliptic equation, first boundary-value problem, unique solvability of a boundary-value problem.
Received: 07.12.2010
Citation:
A. M. Il'in, S. V. Repjevskij, “On the Solvability of a Boundary-Value Problem for an Elliptic Equation”, Mat. Zametki, 92:2 (2012), 216–224; Math. Notes, 92:2 (2012), 197–204
Linking options:
https://www.mathnet.ru/eng/mzm9038https://doi.org/10.4213/mzm9038 https://www.mathnet.ru/eng/mzm/v92/i2/p216
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Abstract page: | 542 | Full-text PDF : | 213 | References: | 91 | First page: | 65 |
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