On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces

By David Colton, Rainer Kress. 2001

97 citations recorded by the source corpus.

Let D⊂ℝ3 be a bounded domain with connected boundary δD of class C2. It is shown that Herglotz wave functions are dense in the space of solutions to the Helmholtz equation with respect to the norm in H1(D) and that the electric fields of electromagnetic Herglotz pairs are dense in the space of solutions to curl curl E=k2E with respect to the norm in Hcurl(D). Two proofs are given in each case, one based on the denseness of the traces of Herglotz wave functions on δD and the other on variational methods. Copyright © 2001 John Wiley & Sons, Ltd.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/14017e162f44cad22e3c742a234f65f93b53ab46

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In Computational Theory and Mathematics

1. David Colton

In Mathematical Physics

1. Houssem Haddar
2. Michele Piana
3. David Colton
4. Andreas Kirsch
5. Fioralba Cakoni

In Mechanics of Materials

1. Houssem Haddar
2. Michele Piana
3. David Colton
4. Andreas Kirsch

Citations in the corpus

• The linear sampling method in inverse electromagnetic scattering theory (2003, background): “An important result concerning Herglotz wavefunctions and their relationship with the solutions of (interior) Dirichlet problems is given in [ 18 , 22].”