Geodesic
THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN
Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 241-249

Voir la notice de l'article provenant de la source Cambridge

DOI

In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is Lipschitz continuous but not differentiable when we consider deformations obtained via a vector field. Our results are illustrated with simple examples.
DOI : 10.1017/S0017089513000219
Mots-clés : 35J60, 35P30 
NAVARRO, J. C.; ROSSI, J. D.; ANTOLIN, A. SAN; SAINTIER, N. THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN. Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 241-249. doi: 10.1017/S0017089513000219
@article{10_1017_S0017089513000219,
     author = {NAVARRO, J. C. and ROSSI, J. D. and ANTOLIN, A. SAN and SAINTIER, N.},
     title = {THE {DEPENDENCE} {OF} {THE} {FIRST} {EIGENVALUE} {OF} {THE} {INFINITY} {LAPLACIAN} {WITH} {RESPECT} {TO} {THE} {DOMAIN}},
     journal = {Glasgow mathematical journal},
     pages = {241--249},
     year = {2014},
     volume = {56},
     number = {2},
     doi = {10.1017/S0017089513000219},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000219/}
}
TY  - JOUR
AU  - NAVARRO, J. C.
AU  - ROSSI, J. D.
AU  - ANTOLIN, A. SAN
AU  - SAINTIER, N.
TI  - THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN
JO  - Glasgow mathematical journal
PY  - 2014
SP  - 241
EP  - 249
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000219/
DO  - 10.1017/S0017089513000219
ID  - 10_1017_S0017089513000219
ER  - 
%0 Journal Article
%A NAVARRO, J. C.
%A ROSSI, J. D.
%A ANTOLIN, A. SAN
%A SAINTIER, N.
%T THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN
%J Glasgow mathematical journal
%D 2014
%P 241-249
%V 56
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000219/
%R 10.1017/S0017089513000219
%F 10_1017_S0017089513000219

Cité par Sources :