Abstract
This paper deals with the eigenvalue problem for the operator L=−Δ−x⋅∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λk of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c>0 and k∈N the following minimization problemmin{λk(Ω):Ωquasi-openset,∫Ωe|x|2/2dx≤c} has a solution.
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.