TY - JOUR
T1 - From neumann to Steklov and beyond, via Robin
T2 - The Weinberger way
AU - Freitas, Pedro
AU - Laugesen, Richard S.
N1 - Publisher Copyright:
© 2021 by Johns Hopkins University Press.
PY - 2021
Y1 - 2021
N2 - The second eigenvalue of the Robin Laplacian is shown to be maximal for the ball among domains of fixed volume, for negative values of the Robin parameter α in the regime connecting the first nontrivial Neumann and Steklov eigenvalues, and even somewhat beyond the Steklov regime. The result is close to optimal, since the ball is not maximal when α is sufficiently large negative, and the problem admits no maximiser when α is positive. 1. Introduction and results. The Robin eigenvalue problem for the.
AB - The second eigenvalue of the Robin Laplacian is shown to be maximal for the ball among domains of fixed volume, for negative values of the Robin parameter α in the regime connecting the first nontrivial Neumann and Steklov eigenvalues, and even somewhat beyond the Steklov regime. The result is close to optimal, since the ball is not maximal when α is sufficiently large negative, and the problem admits no maximiser when α is positive. 1. Introduction and results. The Robin eigenvalue problem for the.
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U2 - 10.1353/ajm.2021.0024
DO - 10.1353/ajm.2021.0024
M3 - Article
AN - SCOPUS:85120849041
SN - 0002-9327
VL - 143
SP - 969
EP - 994
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 3
ER -