From pointwise to local regularity for solutions of Hamilton–Jacobi equations View Full Text


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Article Info

DATE

2014-03

AUTHORS

P. Cannarsa, H. Frankowska

ABSTRACT

It is well-known that solutions to the Hamilton–Jacobi equation fail to be everywhere differentiable. Nevertheless, suppose a solution turns out to be differentiable at a given point in the interior of its domain. May then one deduce that must be continuously differentiable in a neighborhood of ? Although this question has a negative answer in general, our main result shows that it is indeed the case when the proximal subdifferential of at is nonempty. Our approach uses the representation of as the value function of a Bolza problem in the calculus of variations, as well as necessary conditions for such a problem. More... »

PAGES

1061-1074

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00526-013-0611-y

DOI

http://dx.doi.org/10.1007/s00526-013-0611-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046414659


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