Lipschitz Regularity of the Eigenfunctions on Optimal Domains
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605514992 | ||
| 003 | CHVBK | ||
| 005 | 20210128100707.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150401xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-014-0801-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0801-6 | ||
| 245 | 0 | 0 | |a Lipschitz Regularity of the Eigenfunctions on Optimal Domains |h [Elektronische Daten] |c [Dorin Bucur, Dario Mazzoleni, Aldo Pratelli, Bozhidar Velichkov] |
| 520 | 3 | |a We study the optimal sets $${\Omega^\ast\subseteq\mathbb{R}^d}$$ Ω * ⊆ R d for spectral functionals of the form $${F\big(\lambda_1(\Omega),\ldots,\lambda_p(\Omega)\big)}$$ F ( λ 1 ( Ω ) , ... , λ p ( Ω ) ) , which are bi-Lipschitz with respect to each of the eigenvalues $${\lambda_1(\Omega), \lambda_2(\Omega)}, \ldots, {\lambda_p(\Omega)}$$ λ 1 ( Ω ) , λ 2 ( Ω ) , ... , λ p ( Ω ) of the Dirichlet Laplacian on $${\Omega}$$ Ω , a prototype being the problem $$\min{\big\{\lambda_1(\Omega)+\cdots+\lambda_p(\Omega)\;:\;\Omega\subseteq\mathbb{R}^d,\ |\Omega|=1\big\}}.$$ min { λ 1 ( Ω ) + ⋯ + λ p ( Ω ) : Ω ⊆ R d , | Ω | = 1 } . We prove the Lipschitz regularity of the eigenfunctions $${u_1,\ldots,u_p}$$ u 1 , ... , u p of the Dirichlet Laplacian on the optimal set $${\Omega^\ast}$$ Ω * and, as a corollary, we deduce that $${\Omega^\ast}$$ Ω * is open. For functionals depending only on a generic subset of the spectrum, as for example $${\lambda_k(\Omega)}$$ λ k ( Ω ) , our result proves only the existence of a Lipschitz continuous eigenfunction in correspondence to each of the eigenvalues involved. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Bucur |D Dorin |u Laboratoire de Mathématiques (LAMA), Université de Savoie, Campus Scientifique, 73376, Le-Bourget-Du-Lac, France |4 aut | |
| 700 | 1 | |a Mazzoleni |D Dario |u Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata, 1, 27100, Pavia, Italy |4 aut | |
| 700 | 1 | |a Pratelli |D Aldo |u Department Mathematik, Friederich-Alexander Universität Erlangen-Nürnberg, Cauerstrasse, 11, 91058, Erlangen, Germany |4 aut | |
| 700 | 1 | |a Velichkov |D Bozhidar |u Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/1(2015-04-01), 117-151 |x 0003-9527 |q 216:1<117 |1 2015 |2 216 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0801-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0801-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bucur |D Dorin |u Laboratoire de Mathématiques (LAMA), Université de Savoie, Campus Scientifique, 73376, Le-Bourget-Du-Lac, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mazzoleni |D Dario |u Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata, 1, 27100, Pavia, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Pratelli |D Aldo |u Department Mathematik, Friederich-Alexander Universität Erlangen-Nürnberg, Cauerstrasse, 11, 91058, Erlangen, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Velichkov |D Bozhidar |u Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/1(2015-04-01), 117-151 |x 0003-9527 |q 216:1<117 |1 2015 |2 216 |o 205 | ||