Abstract
Let \(d \in \{3,4,5,\ldots\}\). Consider \(L = -\frac{1}{w} \, \operatorname{div}(A \, \nabla u) + \mu\) over its maximal domain in \(L^2_w(\mathbb{R}^d)\). Under certain conditions on the weight \(w\), the coefficient matrix \(A\) and the positive Radon measure \(\mu\) we obtain upper and lower bounds on \(N(\lambda,L)\)–the number of eigenvalues of \(L\) that are at most \(\lambda \ge 1\). Furthermore we show that the eigenfunctions of \(L\) corresponding to those eigenvalues are exponentially decaying. In the course of proofs, we develop generalized Poincaré and weighted Young convolution inequalities as the main tools for the analysis.
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.
