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We study the higher differentiability for nonlinear elliptic equation indivergence form $\mathcal{A}(x,Du)=b(x)$. The result covers the cases in which$\mathcal{A}(x, \xi)$ satisfies $p,q$ growth, with $1<p<2$ in $\xi$ and aSobolev dependence of with respect to $x$. By means of an a-priori estimate weensure the $W^{2,p}_{\mathrm{loc}}(\Omega)$-property for the solution of theboundary value problem.

Higher differentiability for a class of problems under p,q subquadratic growth