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2011, 2011(Special): 1129-1137. doi: 10.3934/proc.2011.2011.1129

Multiple bounded variation solutions of a capillarity problem

Franco Obersnel 1, and  Pierpaolo Omari 1,

1. 

Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy, Italy

Received  July 2010 Revised  August 2010 Published  October 2011

We discuss existence and multiplicity of bounded variation solutions of the non-homogeneous Neumann problem for the prescribed mean curvature equation

-div$(\nabla u/\sqrt(1+|\nablau|^2))=g(x,u)+h$     in $\Omega$
-$\nablau*v/\sqrt(1+|\nablau|^2)=k$         on $\partial\Omega$
where $g(x, s)$ is periodic with respect to $s$. Our approach is variational and makes use of non-smooth critical point theory in the space of bounded variation functions.
Keywords: prescribed mean curvature equation, bounded variation function, Neumann boundary condition, Capillary surface, variational methods.
Mathematics Subject Classification: Primary: 35J25, 35J20, 35J66, 53A10, 49Q20; Secondary: 76B45, 76D45.
Citation: Franco Obersnel, Pierpaolo Omari. Multiple bounded variation solutions of a capillarity problem. Conference Publications, 2011, 2011 (Special) : 1129-1137. doi: 10.3934/proc.2011.2011.1129
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