The embedding method for linear partial differential equations in unbounded and multiply connected domains. (English) Zbl 1106.65101

Summary: The recently suggested embedding method to solve linear boundary value problems [cf. P. N. Shankar, Proc. R. Soc. London A 461, No. 2059, 2121–2133 (2005; Zbl 1153.65369)] is here extended to cover situations where the domain of interest is unbounded or multiply connected. The extension involve the use of complete sets of exterior and interior eigenfunctions on canonical domains. Applications to typical boundary value problems for Laplace’s equation, the Oseen equations and the biharmonic equation are given as examples.


65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J40 Boundary value problems for higher-order elliptic equations


Zbl 1153.65369
Full Text: DOI


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