An a priori Campanato type regularity condition for local minimisers in the calculus of variations

Dodd, Thomas J.. "An a priori Campanato type regularity condition for local minimisers in the calculus of variations." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 111-131. <http://eudml.org/doc/250743>.

@article{Dodd2010,
abstract = { An a priori Campanato type regularity condition is established for a class of W1X local minimisers $\overline\{u\}$ of the general variational integral $ \int_\{\Omega\} F(\nabla u(x))\,\{\rm d\}x$ where $\Omega \subset \mathbb\{R\}^n$ is an open bounded domain, F is of class C2, F is strongly quasi-convex and satisfies the growth condition$ F(\xi)\leq c(1+|\xi|^p)$ for a p > 1 and where the corresponding Banach spaces X are the Morrey-Campanato space $\mathcal\{L\}^\{p,\mu\} (\Omega,\mathbb\{R\}^\{N\times n\})$, µ < n, Campanato space $\mathcal\{L\}^\{p,n\}(\Omega,\mathbb\{R\}^\{N\times n\})$ and the space of bounded mean oscillation $ \{\rm BMO\} \Omega,\mathbb\{R\}^\{N\times n\})$. The admissible maps $u\colon \Omega \to \mathbb\{R\}^N$ are of Sobolev class W1,p, satisfying a Dirichlet boundary condition, and to help clarify the significance of the above result the sufficiency condition for W1BMO local minimisers is extended from Lipschitz maps to this admissible class. },
author = {Dodd, Thomas J.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Calculus of variations; local minimiser; partial regularity; strong quasiconvexity; Campanato space; Morrey space; Morrey-Campanato space; space of bounded mean oscillation; extremals; positive second variation; calculus of variations},
language = {eng},
month = {1},
number = {1},
pages = {111-131},
publisher = {EDP Sciences},
title = {An a priori Campanato type regularity condition for local minimisers in the calculus of variations},
url = {http://eudml.org/doc/250743},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Dodd, Thomas J.
TI - An a priori Campanato type regularity condition for local minimisers in the calculus of variations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/1//
PB - EDP Sciences
VL - 16
IS - 1
SP - 111
EP - 131
AB - An a priori Campanato type regularity condition is established for a class of W1X local minimisers $\overline{u}$ of the general variational integral $ \int_{\Omega} F(\nabla u(x))\,{\rm d}x$ where $\Omega \subset \mathbb{R}^n$ is an open bounded domain, F is of class C2, F is strongly quasi-convex and satisfies the growth condition$ F(\xi)\leq c(1+|\xi|^p)$ for a p > 1 and where the corresponding Banach spaces X are the Morrey-Campanato space $\mathcal{L}^{p,\mu} (\Omega,\mathbb{R}^{N\times n})$, µ < n, Campanato space $\mathcal{L}^{p,n}(\Omega,\mathbb{R}^{N\times n})$ and the space of bounded mean oscillation $ {\rm BMO} \Omega,\mathbb{R}^{N\times n})$. The admissible maps $u\colon \Omega \to \mathbb{R}^N$ are of Sobolev class W1,p, satisfying a Dirichlet boundary condition, and to help clarify the significance of the above result the sufficiency condition for W1BMO local minimisers is extended from Lipschitz maps to this admissible class.
LA - eng
KW - Calculus of variations; local minimiser; partial regularity; strong quasiconvexity; Campanato space; Morrey space; Morrey-Campanato space; space of bounded mean oscillation; extremals; positive second variation; calculus of variations
UR - http://eudml.org/doc/250743
ER -