On the higher differentiability of solutions to a class of variational problems of fast growth

Abstract

We consider the higher differentiability of a solution $u$ to the problem of minimizing $$\int_{\om}[\Lambda(x ,|\nabla v(x)|) +f(x)v(x)]dx$$ where $\Lambda$ is of fast growth in the second variable, i.e., we assume that $\Lambda(x,t)$ grows in $t$ faster than $t^N$, where $N$ is the dimension of the space. We do not assume conditions limiting above the size of the second derivative of $\Lambda$ with respect to $t$.