Accepted Survey paper
Inserted: 31 jul 2013
Last Updated: 5 aug 2013
Journal: Riv. Mat. Univ. Parma
We make a short survey of how the heuristic principle ``the less the measure concentrates, the better the gradient is'' about measure data problems can be implemented for elliptic and parabolic equations of $p$-Laplacian type, both in terms of integrability and differentiability properties. Moreover we prove improved fractional differentiability for the gradient to solution to parabolic equations with linear growth, in the case of Morrey measure data.
Keywords: Morrey spaces, Calderón-Zygmund estimates, Measure data problems