On the singular set of minimizers of p(x)-energies

作者：Tachikawa Atsushi^*

来源：Calculus of Variations and Partial Differential Equations, 2014, 50(1-2): 145-169.

DOI：10.1007/s00526-013-0631-7

We treat the partial regularity of locally bounded local minimizers u for the p(x)- energy functional %26lt;br%26gt;epsilon(nu;Omega) = integral (g(alpha beta) (x) h(ij) (nu) D alpha nu(i) (x) D-beta nu(j)(x)) (p(x)/2) dx, %26lt;br%26gt;defined for maps nu : Omega (subset of R-m) -%26gt; R-n. Assuming the Lipschitz continuity of the exponent p(x) %26gt;= 2, we prove that u epsilon C-1,C-alpha (Omega(0)) for some alpha epsilon (0, 1) and an open set Omega(0) subset of Omega with dim(H)(Omega \ Omega(0)) %26lt;= m - [gamma 1] - 1, where dim(H) stands for the Hausdorff dimension, [gamma 1] the integral part of gamma 1, and gamma 1 = inf p(x).

• 出版日期2014-5