Viscosity solutions, almost everywhere solutions and explicit formulas

Dacorogna, Bernard; Marcellini, Paolo

doi:10.1090/S0002-9947-04-03506-8

Viscosity solutions, almost everywhere solutions and explicit formulas
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by Bernard Dacorogna and Paolo Marcellini

Trans. Amer. Math. Soc. 356 (2004), 4643-4653

DOI: https://doi.org/10.1090/S0002-9947-04-03506-8

Published electronically: January 23, 2004

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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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