# On the existence of variations, possibly with pointwise gradient constraints

Simone Bertone; Arrigo Cellina

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 2, page 331-342
- ISSN: 1292-8119

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topBertone, Simone, and Cellina, Arrigo. "On the existence of variations, possibly with pointwise gradient constraints." ESAIM: Control, Optimisation and Calculus of Variations 13.2 (2007): 331-342. <http://eudml.org/doc/249933>.

@article{Bertone2007,

abstract = {
We propose a necessary and sufficient condition about the existence of variations, i.e.,
of non trivial solutions $\eta\in W^\{1,\infty\}_0(\Omega)$ to the differential inclusion
$\nabla\eta(x)\in-\nabla u(x)+\{\bf D\}$.
},

author = {Bertone, Simone, Cellina, Arrigo},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Variations; differential inclusions; necessary conditions; Differential inclusion},

language = {eng},

month = {5},

number = {2},

pages = {331-342},

publisher = {EDP Sciences},

title = {On the existence of variations, possibly with pointwise gradient constraints},

url = {http://eudml.org/doc/249933},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Bertone, Simone

AU - Cellina, Arrigo

TI - On the existence of variations, possibly with pointwise gradient constraints

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/5//

PB - EDP Sciences

VL - 13

IS - 2

SP - 331

EP - 342

AB -
We propose a necessary and sufficient condition about the existence of variations, i.e.,
of non trivial solutions $\eta\in W^{1,\infty}_0(\Omega)$ to the differential inclusion
$\nabla\eta(x)\in-\nabla u(x)+{\bf D}$.

LA - eng

KW - Variations; differential inclusions; necessary conditions; Differential inclusion

UR - http://eudml.org/doc/249933

ER -

## References

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- L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics19, American Mathematical Society, Providence, Rhode Island (1998). Zbl0902.35002
- L.C. Evans and W. Gangbo, Differential equations methods for the Monge-Kantorovich mass transfer problem, Mem. Amer. Math. Soc.137 (1999) 653. Zbl0920.49004
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- M. Tsuji, On Lindelöf's theorem in the theory of differential equations. Jap. J. Math.16 (1939) 149–161. Zbl0022.13602

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