Regularity of the components in the additive representation of the solution to an elliptic boundary value problem with a point source
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 ${W}^{(2)}_{2}$. The proposed representation allows the use of standard numerical methods without mesh refinement for solving equations with point sources.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Advanced Numerical Methods in Computational Mathematics
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Russian Mathematics
- Issue
- 2
- Pages
- 100–104
- Publication date
- 10 March 2026
- Language
- EN