Lipschitz Regularity of the Eigenfunctions on Optimal Domains

Bucur D, Mazzoleni D, Pratelli A, Velichkov B (2015)

Publication Status: Published

Publication Type: Journal article

Publication year: 2015

Journal

Archive for Rational Mechanics and Analysis Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 216

Pages Range: 117-151

Journal Issue: 1

DOI: 10.1007/s00205-014-0801-6

Abstract

We prove the Lipschitz regularity of the eigenfunctions u(1), ... , u(p) of the Dirichlet Laplacian on the optimal set Omega* and, as a corollary, we deduce that Omega* is open. For functionals depending only on a generic subset of the spectrum, as for example lambda(k)(Omega), our result proves only the existence of a Lipschitz continuous eigenfunction in correspondence to each of the eigenvalues involved.

Authors with CRIS profile

Aldo Pratelli Lehrstuhl für Analysis

Involved external institutions

University of Savoy Mont Blanc / Université Savoie Mont Blanc FR France (FR) Università degli Studi di Pavia IT Italy (IT) Scuola Normale Superiore di Pisa (SNS) IT Italy (IT)

How to cite

APA:

Bucur, D., Mazzoleni, D., Pratelli, A., & Velichkov, B. (2015). Lipschitz Regularity of the Eigenfunctions on Optimal Domains. Archive for Rational Mechanics and Analysis, 216(1), 117-151. https://dx.doi.org/10.1007/s00205-014-0801-6

MLA:

Bucur, Dorin, et al. "Lipschitz Regularity of the Eigenfunctions on Optimal Domains." Archive for Rational Mechanics and Analysis 216.1 (2015): 117-151.

BibTeX: Download