`a`

On a result of C.V. Coffman and W.K. Ziemer about the prescribed mean curvature equation

Pages: 1138 - 1147, Issue Special, September 2011

 Abstract        Full Text (332.3K)              

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 produce a detailed proof of a result of C.V. Co ffman and W.K. Ziemer [1] on the existence of positive solutions of the Dirichlet problem for the prescribed mean curvature equation

-div$(\nablau/\sqrt(1+|\nablau|^2)=\lambdaf(x,u)$ in $\Omega,$     $u=0$ on $\partial\Omega$
assuming that $f$ has a superlinear behaviour at $u = 0$.

Keywords:  Prescribed mean curvature equation, Dirichlet problem, positive solution, variational method, Nehari method.
Mathematics Subject Classification:  Primary: 35J25, 35J20, 35J60

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