We prove local Calderón–Zygmund estimates for weak solutions of the evolutionary -Laplacian system
under the classical hypothesis of logarithmic continuity for the variable exponent . More precisely, we show that the spatial gradient of the solution is as integrable as the right-hand side , i.e.,
together with quantitative estimates. Thereby we allow the presence of eventually discontinuous coefficients , requiring only a VMO condition with respect to the spatial variable .
Cite this article
Paolo Baroni, Verena Bögelein, Calderón–Zygmund estimates for parabolic -Laplacian systems. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1355–1386DOI 10.4171/RMI/817