Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals

Abstract We prove the higher differentiability of integer order of locally bounded minimizers of integral functionals of the form $$\begin{aligned} \mathcal {F}(u,\Omega ):= \,\sum _{i=1}^{n} \dfrac{1}{p_i}\displaystyle \int _\Omega \, a_i(x) |u_{x_i} |^{p_i} dx- \int _\Omega \omega (x)u(x) dx, \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mstyle> <mml:mrow> <mml:mi>F</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>u</mm