Abstract
In this paper, we use the finite difference argument to prove a higher fractional differentiability in the scale of Besov spaces for the gradients of solutions of the double phase elliptic problems with unilateral obstacle:∫Ω〈A(x,Du),D(u−v)〉dx≤∫Ω〈|F|p−2F+a(x)|F|q−2F,D(u−v)〉dx. A key feature of our study consists in assuming that the nonlinearity A(x,Du) has an anisotropic (p,q)-growth for any 2≤p<q and qp<1+αn with 0≤a(⋅)∈C0,α(Ω‾) for α∈(0,1].
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