Regularity of the Components in the Additive Representation of the Solution to an Elliptic Boundary Value Problem with a Point Source

G. O. Trifonova

doi:10.3103/s1066369x26700192

February 1, 2026Russian Mathematics

Regularity of the Components in the Additive Representation of the Solution to an Elliptic Boundary Value Problem with a Point Source

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Key Points

The research aims to develop an additive representation for solving elliptic boundary value problems that incorporates point sources and to establish the regularity of the solution.
Derivation of an additive representation for the solution to the elliptic problem.
Formulation of the unknown component's problem focusing on its smoothness.
Analysis of the solution's membership in the Sobolev space W_{2}^{(2)}.
The developed additive representation isolates the singularity from the point source, enhancing solution techniques.
The solution exists in Sobolev space W_{2}^{(2)}, indicating sufficient regularity.
Standard numerical methods can be employed without requiring mesh refinement.

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Implication

Regularity of additive representation improves solving elliptic problems with point sources, suggesting efficient numerical approaches.

Abstract

A new additive representation has been obtained for solving an elliptic problem with a point source, explicitly isolating the singularity caused by the presence of the source. A problem for the unknown component of the decomposition is formulated, and the smoothness of its solution is established, namely, its membership in the Sobolev space W₂^(2) . The proposed representation allows the use of standard numerical methods without mesh refinement for solving equations with point sources.

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G. O. Trifonova (2026) studied this question.

synapsesocial.com/papers/6a17daf83fad632b0f9d7e24 https://doi.org/10.3103/s1066369x26700192

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Regularity of the Components in the Additive Representation of the Solution to an Elliptic Boundary Value Problem with a Point Source

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Regularity of the Components in the Additive Representation of the Solution to an Elliptic Boundary Value Problem with a Point Source

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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