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Viscosity solutions, almost everywhere solutions and explicit formulas
Author(s):
Bernard
Dacorogna;
Paolo
Marcellini
Journal:
Trans. Amer. Math. Soc.
356
(2004),
4643-4653.
MSC (2000):
Primary 34A60, 35F30, 49L25
Posted:
January 23, 2004
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Abstract:
Consider the differential inclusion  in  . 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.
References:
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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:
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
Posted:
January 23, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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