Higher Differentiability of Minimizers for Non-Autonomous Orthotropic Functionals

We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals {equation*} F(u,Ω):= \, ∫_Ω ∑ᵢ₌₁ⁿ \, a_i(x) ux_i p_i dx, {equation*} with exponents pᵢ ≥ 2 and with coefficients aᵢ(x) that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents pᵢ, which depends on the dimension and on the degree of regularity of the coefficients aᵢ(x)