We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals equation* F (u, ): = \, _ ₈=₁^n \, aᵢ (x) uₗ㶁 ^pᵢ 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)
Stefania Russo (Sun,) studied this question.