Asymmetric Poincaré inequalities and solvability of capillarity problems

In this paper we first establish an asymmetric version of the Poincaré inequality in the space of bounded variation functions, and then, basically relying on this result, we discuss the existence, the non-existence and the multiplicity of bounded variation solutions of a class of capillarity problem...

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Bibliographic Details
Published in:Journal of functional analysis 2014-08, Vol.267 (3), p.842-900
Main Authors: Obersnel, Franco, Omari, Pierpaolo, Rivetti, Sabrina
Format: Article
Language:English
Subjects:
Ahmad–Lazer–Paul condition
Bounded variation function
Capillarity equation
Existence and multiplicity
Hammerstein condition
Landesman–Lazer condition
Mean curvature
Non-existence
Non-smooth critical point theory
Poincaré inequality
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Summary:In this paper we first establish an asymmetric version of the Poincaré inequality in the space of bounded variation functions, and then, basically relying on this result, we discuss the existence, the non-existence and the multiplicity of bounded variation solutions of a class of capillarity problems with asymmetric perturbations.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2014.03.011