Erratum to: Isoperimetric Inequalities for the Principal Eigenvalue of a Membrane and the Energy of Problems with Robin Boundary Conditions

Catherine Bandle; Alfred Wagner

doi:10.68381/jca26048

Abstract

A correct version of Lemma 2.3 and Theorem 2.4 in Isoperimetric Inequalities for the Principal Eigenvalue of a Membrane and the Energy of Problems with Robin Boundary Conditions [J. Convex Analysis 22(3) (2015) 627–640] is presented.

Author information

Contact details are reproduced from the original publication and may be historical.

Catherine Bandle

Dep. Mathematik und Informatik, Universität Basel, 4051 Basel, Switzerland

catherine.bandle@unibas.ch

Alfred Wagner

Institut für Mathematik, RWTH Aachen, 52062 Aachen, Germany

wagner@instmath.rwth-aachen.de

Keywords

Erratum
Rayleigh-Faber Krahn inequality
Robin boundary conditions
domain variation
harmonic transplantation

Mathematics Subject Classification

49K20, 49R05, 15A42, 35J20, 35N25

References

C. Bandle, M. Flucher: Harmonic radius and concentration of energy; hyperbolic radius and Liouville’s equations ∆U = eU and ∆U = U (n+2)/(n−2), SIAM Review 38 (1969) 191–238.https://doi.org/10.1137/1038039 Google Scholar
C. Bandle, A. Wagner: Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions, J. Convex Analysis 22(3) (2015) 627–640.https://doi.org/10.68381/jca22031 Google Scholar
C. Bandle, A. Wagner: Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues, Adv. Nonlinear Analysis 7 (2018) 49–66.https://doi.org/10.1515/anona-2015-0171 Google Scholar
P. Cardaliaguet, R. Tahraoui: On the strict concavity of the harmonic radius in dimension N ≥ 3, J. Math. Pures Appl. (9) 81(2) (2002) 223–240.https://doi.org/10.1016/S0021-7824(01)01246-6 Google Scholar
J. Hersch: Transplantation harmonique, transplantation par modules, et théorèmes isopérimétriques, Comment. Math. Helv. 44 (1969) 354–366.https://doi.org/10.1007/BF02564535 Google Scholar

Suggested citation

Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.

[1] C. Bandle, M. Flucher: Harmonic radius and concentration of energy; hyperbolic radius and Liouville’s equations ∆U = eU and ∆U = U (n+2)/(n−2), SIAM Review 38 (1969) 191–238.https://doi.org/10.1137/1038039 Google Scholar

[2] C. Bandle, A. Wagner: Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions, J. Convex Analysis 22(3) (2015) 627–640.https://doi.org/10.68381/jca22031 Google Scholar

[3] C. Bandle, A. Wagner: Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues, Adv. Nonlinear Analysis 7 (2018) 49–66.https://doi.org/10.1515/anona-2015-0171 Google Scholar

[4] P. Cardaliaguet, R. Tahraoui: On the strict concavity of the harmonic radius in dimension N ≥ 3, J. Math. Pures Appl. (9) 81(2) (2002) 223–240.https://doi.org/10.1016/S0021-7824(01)01246-6 Google Scholar

[5] J. Hersch: Transplantation harmonique, transplantation par modules, et théorèmes isopérimétriques, Comment. Math. Helv. 44 (1969) 354–366.https://doi.org/10.1007/BF02564535 Google Scholar