Calderón–Zygmund estimates for parabolic -Laplacian systems

  • Paolo Baroni

    Uppsala University, Sweden
  • Verena Bögelein

    Universität Salzburg, Austria


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. 1355–1386

DOI 10.4171/RMI/817