Abstract
Consider the Stekloff eigenvalue problem \[\begin{gathered} \Delta ^2 u = 0\quad {\text{in }}R, \hfill \\ u = \Delta u - q\tfrac{{\partial u}}{{\partial n}} = 0\quad {\text{on }}\partial R \hfill. \\ \end{gathered} \] It will be shown that the first eigenvalue is simple, and its eigenfunction does not change sign. Bounds for the first eigenvalue are discussed, particularly for the square, and a conjecture is disproved.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.