On continuity of minimizers for certain quadratic growth functionals
RAGUSA, Maria Alessandra ; TACHIKAWA, Atsushi
J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 691-700 / Harvested from Project Euclid
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In this paper we treat the regularity problem for minimizers $u(x) : \Omega \subset \mathbf{R}^m \to \mathbf{R}^n$ of quadratic growth functionals $\int_\Omega A(x,u,Du)dx$ . About the dependence on the variable $x$ we assume only that $A(\cdot , u, p)$ is in the class $VMO$ as a function of $x$ . Namely, we do not assume the continuity of $A(x,u,p)$ with respect to $x$ . We will prove a partial regularity result for the case $m \leq 4$ .
Publié le : 2005-07-14
Classification:  variational problem,  minimizer,  partial regularity,  35J50,  35B65,  46E30,  35R05 
@article{1158241929,
     author = {RAGUSA, Maria Alessandra and TACHIKAWA, Atsushi},
     title = {On continuity of minimizers for certain quadratic growth functionals},
     journal = {J. Math. Soc. Japan},
     volume = {57},
     number = {4},
     year = {2005},
     pages = { 691-700},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1158241929}
}

RAGUSA, Maria Alessandra; TACHIKAWA, Atsushi. On continuity of minimizers for certain quadratic growth functionals. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp.  691-700. http://gdmltest.u-ga.fr/item/1158241929/