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

Franco Obersnel; Pierpaolo Omari

doi:10.3934/proc.2011.2011.1138

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2011, Volume 2011: 1138-1147. Doi: 10.3934/proc.2011.2011.1138 open access

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

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

Received: June 30, 2010

Revised: July 31, 2011

Published: August 2017

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Abstract

We produce a detailed proof of a result of C.V. Coffman 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 $u = 0$.

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Mathematics Subject Classification: Primary: 35J25, 35J20, 35J60.

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