Gradient estimates for double phase problems with two modulating coefficients

In this paper, we consider a class of non-uniformly elliptic equations whose model is given by (Formula presented.) where 1<p<q, a(·),b(·)≥0 and 0<μ≤a(·)+b(·). Here, the modulating coefficient b(·) is assumed to be Hölder continuous and the modulating coefficient a(·) is assumed to be uniformly continuous. We prove the following regularity result with non-standard growth conditions: (Formula presented.) and establish the corresponding gradient estimates.