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Multiple bounded variation solutions of a capillarity problem

Pages: 1129 - 1137, Issue Special, September 2011

 Abstract        Full Text (331.3K)              

Franco Obersnel - Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy (email)
Pierpaolo Omari - Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy (email)

Abstract: 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:  Capillary surface, prescribed mean curvature equation, Neumann boundary condition, bounded variation function, variational methods
Mathematics Subject Classification:  Primary: 35J25, 35J20, 35J66, 53A10, 49Q20; Secondary: 76B45, 76D45

Received: July 2010;      Revised: August 2010;      Published: October 2011.