Clop, AlbertGentile, AndreaPassarelli di Napoli, Antonia2025-06-102025-06-102023-05-291664-3607https://hdl.handle.net/2445/221444We prove a sharp higher differentiability result for local minimizers of functionals of the form $$ \mathscr{F}(w, \Omega)=\int_{\Omega}[F(x, D w(x))-f(x) \cdot w(x)] d x $$ with non-autonomous integrand $F(x, \xi)$ which is convex with respect to the gradient variable, under $p$-growth conditions, with $1<p<2$. The main novelty here is that the results are obtained assuming that the partial map $x \mapsto D_{\xi} F(x, \xi)$ has weak derivatives in some Lebesgue space $L^q$ and the datum $f$ is assumed to belong to a suitable Lebesgue space $L^r$. We also prove that it is possible to weaken the assumption on the datum $f$ and on the map $x \mapsto D_{\xi} F(x, \xi)$, if the minimizers are assumed to be a priori bounded.55 p.application/pdfengcc-by (c) Clop et al., 2023http://creativecommons.org/licenses/by/4.0/Funcions convexesEquacions diferencials el·líptiquesTeoria de controlConvex functionsElliptic differential equationsControl theoryinfo:eu-repo/semantics/article7587172025-06-10info:eu-repo/semantics/openAccess