Atsushi Tachikawa

Partial regularity of p(x)-harmonic maps

Let

Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure

(g^{alphabeta}(x))

On interior regularity of minimizers of p(x)-energy functionals

and

On continuity of minimizers for certain quadratic growth functionals

(h_{ij}(u))

Boundary regularity of minimizers of p(x)-energy functionals

be uniformly elliptic symmetric matrices, and assume that

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

h_{ij}(u)

Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth

and

Partial regularity results up to the boundary for harmonic maps into a Finsler manifold

p(x) , (, geq 2)

Regularity results up to the boundary for minimizers of p(x)-energy with \(p(x)>1\)

are sufficiently smooth. We prove partial regularity of minimizers for the functional [ n{mathcal F}(u) = int_Omega (g^{alpha beta}(x) h_{ij}(u) nD_alpha u^iD_beta u^j)^{p(x)/2} dx, ] under the non-standard growth conditions of

ESTIMATES OF THE DERIVATIVES OF MINIMIZERS OF A SPECIAL CLASS OF VARIATIONAL INTEGRALS

p(x)