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Boundary Integral Equations for Mixed Boundary Value Problems in R 3
Author(s) -
Stephan Ernst P.
Publication year - 1987
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19871340103
Subject(s) - mathematics , mathematical analysis , integral equation , neumann boundary condition , mixed boundary condition , boundary value problem , robin boundary condition , helmholtz equation , dirichlet distribution , dirichlet problem
Both exterior and interior mixed Dirichlet‐Neumann problems in R 3 for the scalar Helmholtz equation are solved via boundary integral equations. The integral equations are equivalent to the original problem in the sense that the traces of the weak seolution satisfy the integral equations, and, conversely, the solution of the integral equations inserted into Green's formula yields the solution of the mixed boundary value problem. The calculus of pseudodifferential operators is used to prove existence and regularity of the solution of the integral equations. The regularity results — obtained via Wiener‐Hopf technique — show the explicit “edge” behavior of the solution near the submanifold which separates the Dirichlet boundary from the Neumann boundary.