Universität zu Köln

Crasta, Graziano, Fragala, Ilaria and Kawohl, Bernd ORCID: 0000-0003-2918-7318 (2020). ON THE FIRST EIGENVALUE OF THE NORMALIZED p-LAPLACIAN. Proc. Amer. Math. Soc., 148 (2). S. 577 - 591. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6826

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Abstract

We prove that if Omega is an open bounded domain with smooth and connected boundary, for every p is an element of (1,+infinity) the first Dirichlet eigenvalue of the normalized p-Laplacian is simple in the sense that two positive eigenfunctions are necessarily multiple of each other. We also give a (nonoptimal) lower bound for the eigenvalue in terms of the measure of Omega, and we address the open problem of proving a Faber-Krahn-type inequality with balls as optimal domains.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Crasta, Graziano UNSPECIFIED UNSPECIFIED UNSPECIFIED Fragala, Ilaria UNSPECIFIED UNSPECIFIED UNSPECIFIED Kawohl, Bernd UNSPECIFIED orcid.org/0000-0003-2918-7318 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-346831
DOI:	10.1090/proc/14823
Journal or Publication Title:	Proc. Amer. Math. Soc.
Volume:	148
Number:	2
Page Range:	S. 577 - 591
Date:	2020
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6826
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TUG-OF-WAR; MAXIMUM PRINCIPLE; VISCOSITY SOLUTIONS; INFINITY; REGULARITY; DIRICHLET; DOMAINS Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/34683