Calculus of Variations and Geometric Measure Theory

P. Baroni

Nonlinear parabolic equations with Morrey data

created by baroni on 31 Jul 2013
modified on 05 Aug 2013


Accepted Survey paper

Inserted: 31 jul 2013
Last Updated: 5 aug 2013

Journal: Riv. Mat. Univ. Parma
Volume: 5
Number: 1
Year: 2014


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