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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Viscosity solutions, almost everywhere solutions and explicit formulas


Authors: Bernard Dacorogna and Paolo Marcellini
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4643-4653
MSC (2000): Primary 34A60, 35F30, 49L25
Published electronically: January 23, 2004
MathSciNet review: 2067137
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Abstract: Consider the differential inclusion $Du\in E$ in $\mathbb{R} ^{n}$. We exhibit an explicit solution that we call fundamental. It also turns out to be a viscosity solution when properly defining this notion. Finally, we consider a Dirichlet problem associated to the differential inclusion and we give an iterative procedure for finding a solution.


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Additional Information

Bernard Dacorogna
Affiliation: Départment de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Email: bernard.dacorogna@epfl.ch

Paolo Marcellini
Affiliation: Dipartimento di Matematica U. Dini, Università di Firenze, Firenze, Italy
Email: marcell@math.unifi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03506-8
PII: S 0002-9947(04)03506-8
Keywords: Almost everywhere solutions, viscosity solutions of nonlinear first order partial differential equations
Received by editor(s): December 2, 2002
Received by editor(s) in revised form: August 21, 2003
Published electronically: January 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society