Michael Ruzhansky, Makhmud Sadybekov, Durvudkhan Suragan
Chapman and Hall/CRC
March 2, 2020 Forthcoming
Reference - 366 Pages
ISBN 9781138360716 - CAT# K396262
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations.
Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains.
1. Function spaces. 2. Foundations of linear operator theory. 3. Elements of the spectral theory of differential operators. 4. Symmetric decreasing rearrangements and applications. 5. Inequalities of spectral geometry.