Calderón–Zygmund estimates for general elliptic operators with double phase. (May 2020) - Shin, Pilsoo
Abstract: We derive Calderón–Zygmund type estimates for the gradient of bounded distributional solutions to the problem div b ( x, u ) | D u | p − 2 D u + a ( x ) | D u | q − 2 D u = div | F | p − 2 F + a ( x ) | F | q − 2 F where 1 < p < q and 0 ≤ a ( ⋅ ) ∈ C α . The coefficient b ( x, z ) is supposed to be small-BMO with respect to x and merely continuous in z .