Abstract
Characterizations of eigenvalues and eigenfunctions of the Laplacian on a product domain Ωp:=Ω1×Ω2 are obtained. When zero Dirichlet, Robin or Neumann conditions are specified on each factor, then the eigenfunctions on Ωp are precisely the products of the eigenfunctions on the sets Ω1, Ω2 separately. There is a related result when Steklov boundary conditions are specified on Ω2. These results enable the characterization of H1(Ωp) and H01(Ωp) as tensor products and descriptions of some orthogonal bases of the spaces. A different characterization of the trace space of H1(Ωp) is found.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
