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On the strong maximum principle

Author(s): Arrigo Cellina
Journal: Proc. Amer. Math. Soc. 130 (2002), 413-418.
MSC (1991): Primary 35B50, 49N60
Posted: May 23, 2001
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Abstract: This paper presents a necessary and sufficient condition on the convex function in order that continuous solutions to

$\begin{displaymath}\hbox {minimize} \int _{\Omega } f(\Vert\nabla u(x)\Vert) \, dx \hbox { on } u^{0} + W^{1,1}_{0}(\Omega )\end{displaymath}$

satisfy a Strong Maximum Principle on any open connected $\Omega$ .

References:

1.: A. Cellina, On the Bounded Slope Condition and the validity of the Euler Lagrange equation, SIAM J. Control Optim., to appear.
2.: D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1983. MR 86c:35035
3.: C. Mariconda and G. Treu, A comparison principle for minimizers, C.R. Acad. Sci. Paris Sér. I Math. 330 (2000), 681-686. CMP 2000:14
4.: G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. MR 92b:35004

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Additional Information:

Arrigo Cellina
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Viale Sarca 202, 20126 Milano, Italy
Email: cellina@matapp.unimib.it

DOI: 10.1090/S0002-9939-01-06104-4
PII: S 0002-9939(01)06104-4
Keywords: Strong Maximum Principle, Comparison Theorem.
Received by editor(s): March 2, 2000
Received by editor(s) in revised form: June 13, 2000
Posted: May 23, 2001
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2001, American Mathematical Society


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