We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-2,
author = {Giuseppe Buttazzo and Bozhidar Velichkov},
title = {Some new problems in spectral optimization},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {19-35},
zbl = {1293.49105},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-2}
}
Giuseppe Buttazzo; Bozhidar Velichkov. Some new problems in spectral optimization. Banach Center Publications, Tome 102 (2014) pp. 19-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-2/