In the present paper we consider spectral optimization problems involving the Schr\"odinger operator $-\Delta +\mu$ on $R^d$, the prototype being the minimization of the $k$ the eigenvalue $\lambda_k(\mu)$. Here $\mu$ may be a capacitary measure with prescribed torsional rigidity (like in the Kohler-Jobin problem) or a classical nonnegative potential $V$ which satisfies the integral constraint $\int V^{-p}dx \le m$ with $0<p<1$. We prove the existence of global solutions in $R^d$ and that the optimal potentials or measures are equal to $+\infty$ outside a compact set.
Autori interni: | |
Autori: | Bucur, D.; Buttazzo, Giuseppe; Velichkov, B. |
Titolo: | Spectral optimization problems for potentials and measures |
Anno del prodotto: | 2014 |
Digital Object Identifier (DOI): | 10.1137/130939808 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
reprint_SIMA.pdf | Versione finale editoriale | Tutti i diritti riservati (All rights reserved) | Open AccessVisualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.