Calculus of Variations and Geometric Measure Theory
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B. Dacorogna - A. Ferriero

Regularity and selecting principles for Implicit ODEs

created by ferrieroa on 19 Apr 2007
modified on 15 Jun 2010

[BibTeX]

Published Paper

Inserted: 19 apr 2007
Last Updated: 15 jun 2010

Journal: Discrete Cont. Dyn. Syst. Ser. B
Year: 2009

Abstract:

Implicit Ordinary or Partial Differential Equations have been widely studied in recent times, essentially from the existence of solutions point of view. One of the main issues is to select a meaningful solution among the infinitely many ones. The most celebrated principle is the viscosity method. This selection principle is well adapted to convex Hamiltonians, but is not always applicable to the non-convex setting.

In this work we present an alternative selecting principle that singles out the most regular solutions (which do not always coincide with the viscosity ones). Our method is based on a general regularity theorem for Implicit ODEs. We also provide several examples.

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