# A regularity result for a convex functional and bounds for the singular set

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 4, page 1002-1017
- ISSN: 1292-8119

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topDe Maria, Bruno. "A regularity result for a convex functional and bounds for the singular set." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 1002-1017. <http://eudml.org/doc/250746>.

@article{DeMaria2010,

abstract = {
In this paper we prove a regularity
result for local minimizers of functionals of the Calculus of Variations of the
type$$
\int\_\{\Omega\}f(x, Du)\ \{\rm d\}x
$$where Ω is a bounded open set in $\mathbb\{R\}^\{n\}$, u∈$W^\{1,p\}_\{\rm loc\}$(Ω; $\mathbb\{R\}^\{N\}$), p> 1, n≥ 2 and N≥ 1.
We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give
a bound on the Hausdorff dimension of the singular set of minimizers.
},

author = {De Maria, Bruno},

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

keywords = {Partial regularity; singular sets; fractional differentiability; variational integrals; partial regularity},

language = {eng},

month = {10},

number = {4},

pages = {1002-1017},

publisher = {EDP Sciences},

title = {A regularity result for a convex functional and bounds for the singular set},

url = {http://eudml.org/doc/250746},

volume = {16},

year = {2010},

}

TY - JOUR

AU - De Maria, Bruno

TI - A regularity result for a convex functional and bounds for the singular set

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/10//

PB - EDP Sciences

VL - 16

IS - 4

SP - 1002

EP - 1017

AB -
In this paper we prove a regularity
result for local minimizers of functionals of the Calculus of Variations of the
type$$
\int_{\Omega}f(x, Du)\ {\rm d}x
$$where Ω is a bounded open set in $\mathbb{R}^{n}$, u∈$W^{1,p}_{\rm loc}$(Ω; $\mathbb{R}^{N}$), p> 1, n≥ 2 and N≥ 1.
We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give
a bound on the Hausdorff dimension of the singular set of minimizers.

LA - eng

KW - Partial regularity; singular sets; fractional differentiability; variational integrals; partial regularity

UR - http://eudml.org/doc/250746

ER -

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