# name
Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions

# metadata.dc.description.abstract[].value
We 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.

# metadata.dc.relation.ispartof[].value
Bulletin Of Mathematical Sciences, 2023, vol. 13, num.2

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions