We prove the existence of at least two solutions to the Plateau problem for any curvature function H close enough, in L^∞-norm, to a nonzero constant H_0 such that ∣H_0∣.∣∣γ∣∣ <1, where ∣∣γ∣∣ denotes the L^∞-norm of the boundary condition γ.
Publié le : 1994-07-04
Classification:
Plateau problem,
Mean curvature,
Nonlinear elliptic PDEs,
Noncompact variational problems,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00943475,
author = {Bethuel, Fabrice and Rey, Olivier},
title = {Multiple solutions to the Plateau problem for nonconstant mean curvature},
journal = {HAL},
volume = {1994},
number = {0},
year = {1994},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00943475}
}
Bethuel, Fabrice; Rey, Olivier. Multiple solutions to the Plateau problem for nonconstant mean curvature. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/hal-00943475/