Calculus of Variations and Geometric Measure Theory

G. Buttazzo - B. Velichkov

Some New Problems in Spectral Optimization

created by velichkov on 13 Dec 2012
modified on 31 Jan 2013



Inserted: 13 dec 2012
Last Updated: 31 jan 2013

Year: 2012


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-Carath ́odory 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 an optimization problem for Schr\"odinger potentials in suitable classes.