*Published Paper*

**Inserted:** 28 sep 2012

**Last Updated:** 16 nov 2012

**Journal:** Houston J. Math.

**Volume:** 38

**Number:** 3

**Pages:** 855-914

**Year:** 2012

**Abstract:**

We prove sharp Lorentz- and Morrey-space estimates for the gradient of solutions $u$ to nonlinear parabolic equations of the type \[u_t - {\rm div}\, a(z,Du) = g, \qquad \mbox{ on } \Omega_T = \Omega \times (-T,0),\] where the vector field $a$ is assumed to satisfy classical growth and ellipticity conditions and where the inhomogeneity $g$ is only assumed to be integrable to some power $\gamma > 1$. In particular we investigate the case where $\gamma$ stays below the exponent allowing for weak solutions $u \in L^2(-T,0;W^{1,2}(\Omega))$.

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