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Mat. Zametki, 2012, Volume 92, Issue 2, Pages 216–224 (Mi mz9038)  

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

DOI: https://doi.org/10.4213/mzm9038

Full text: PDF file (422 kB)
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English version:
Mathematical Notes, 2012, 92:2, 197–204

Bibliographic databases:

Document Type: Article
UDC: 517.928
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

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