Abstract
We prove the partial Hölder continuity for minimizers of quasiconvex functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\textrm{d} x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to the $x$-variable and is continuous with respect to ${\bf u}$. The growth condition with respect to the gradient variable is assumed a general one.
Highlights
In this paper we study the partial regularity of minimizers of the integral functional
The growth conditions we impose on f = f (x, u, P) are quite general, being as they permit ‘general growth condition’ with respect to the gradient variable
We prove by induction the first inequality in (3.39) for m + 1
Summary
In this paper we study the partial regularity of minimizers of the integral functional. The growth conditions we impose on f = f (x, u, P) are quite general, being as they permit ‘general growth condition’ with respect to the gradient variable. This allows us to treat in a unified way the degenerate (when p > 2) or singular (when p < 2) behaviour. Theorem 1.1, proves that a minimizer of (1.1) is locally Holder continuous for any Holder exponent 0 < α < 1; i.e., if u is a minimizer of (1.1), u ∈ Cl0o,cα(Ω0, RN ), where Ω0 ⊂ Ω is an open set of full measure specified in the statement of theorem 1.1 later
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