Energy estimates of harmonic maps between Riemannian manifolds

Abstract

Let $\Omega \subset R^n,$ $n\ge 3,$ be a bounded open set, $x=(x_1,x_2,\dots ,x_n)$ a generic point which belongs to $\Omega ,$ $u:\Omega \to R^N,$ $N>1,$ and $Du=(D_{\alpha }{u}^i)$, $D_{\alpha }=\partial /\partial x_{\alpha },$ $\alpha =1,\dots ,n,$ $i=1,\dots ,N.$ Main goal is the study of regularity of the minima of nondifferentiable functionals $$\mathcal{F}={\int }_{\Omega }F(x,u,Du)dx.$$ having the integrand function different shapes of smoothness. The method is based on the use some majorizations for the functional, rather than the well known Euler equation associated to it.

References in corpus (1)

• Interior estimates in Campanato spaces related to quadratic functionals