On the strong maximum principle
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- by Arrigo Cellina PDF
- Proc. Amer. Math. Soc. 130 (2002), 413-418 Request permission
Abstract:
This paper presents a necessary and sufficient condition on the convex function $f$ in order that continuous solutions to \[ \operatorname {minimize} \int _{\Omega } f(\|\nabla u(x)\|) dx \mathrm { on }\; u^{0} + W^{1,1}_{0}(\Omega )\] satisfy a Strong Maximum Principle on any open connected $\Omega$.References
- A. Cellina, On the Bounded Slope Condition and the validity of the Euler Lagrange equation, SIAM J. Control Optim., to appear.
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0
- C. Mariconda and G. Treu, A comparison principle for minimizers, C.R. Acad. Sci. Paris Sér. I Math. 330 (2000), 681–686.
- Giovanni Maria Troianiello, Elliptic differential equations and obstacle problems, The University Series in Mathematics, Plenum Press, New York, 1987. MR 1094820, DOI 10.1007/978-1-4899-3614-1
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
- Received by editor(s): March 2, 2000
- Received by editor(s) in revised form: June 13, 2000
- Published electronically: May 23, 2001
- Communicated by: David S. Tartakoff
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 413-418
- MSC (1991): Primary 35B50, 49N60
- DOI: https://doi.org/10.1090/S0002-9939-01-06104-4
- MathSciNet review: 1862120