Symmetry of intrinsically singular solutions of double phase problems

where Ω ⊂ R , 1 < p < q < N and a(·) ≥ 0. This class of functionals naturally appear in homogenization theory and in the study of strongly anisotropic materials (see, e.g., [39]), and falls into the framework of the so called functionals with non-standard growth introduced by Marcellini [27, 28]. The literature concerning functionals like (1.1) is pretty vast and concerns as a main topic the regularity of minimizers, see e.g. [2, 11, 12, 23] and the references therein.