AN ISOPERIMETRIC INEQUALITY FOR THE FIRST STEKLOV-DIRICHLET LAPLACIAN EIGENVALUE OF CONVEX SETS WITH A SPHERICAL HOLE

Gavitone N, Paoli G, Piscitelli G, Sannipoli R (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Pacific Journal of Mathematics

Book Volume: 320

Pages Range: 241-259

Journal Issue: 2

DOI: 10.2140/pjm.2022.320.241

Abstract

We prove the existence of a maximum for the first Steklov-Dirichlet eigenvalue in the class of convex sets with a fixed spherical hole, under volume constraint. More precisely, if Omega = Omega(0) \ (B) over bar (R1), where B-R1 is the ball centered at the origin with radius R-1 > 0 and Omega(0) subset of R-n, n >= 2, is an open, bounded and convex set such that BR1 (sic) Omega(0), then the first Steklov-Dirichlet eigenvalue sigma(1)(Omega) has a maximum when R-1 and the measure of Omega are fixed. Moreover, if Omega(0) is contained in a suitable ball, we prove that the spherical shell is the maximum.

Authors with CRIS profile

Gloria Paoli Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Gavitone, N., Paoli, G., Piscitelli, G., & Sannipoli, R. (2022). AN ISOPERIMETRIC INEQUALITY FOR THE FIRST STEKLOV-DIRICHLET LAPLACIAN EIGENVALUE OF CONVEX SETS WITH A SPHERICAL HOLE. Pacific Journal of Mathematics, 320(2), 241-259. https://dx.doi.org/10.2140/pjm.2022.320.241

MLA:

Gavitone, Nunzia, et al. "AN ISOPERIMETRIC INEQUALITY FOR THE FIRST STEKLOV-DIRICHLET LAPLACIAN EIGENVALUE OF CONVEX SETS WITH A SPHERICAL HOLE." Pacific Journal of Mathematics 320.2 (2022): 241-259.

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