| Abstract: |
| Is showed a problem studied in cooperation with Professor Atsushi Tachikawa.
We treat the regularity problem for minimizers of quadratic and nonquadratic growth functionals where the integrand is dependent on x,u, Du. We poit out that about the dependence on the variable x is assumed only that A( ,u, p) is in the class VMO, Vanishing Mean Oscillation class, as a function of x.
Namely, is not assumed the continuity of A(x, u, p) with respect to x.
Are considered both partial and global regularity of the minimizer $u$.
Keywords:: minimizer, partial and boundary regularity
MSC2010 Classification: 49N60, 35J50. |
|