Riv. Mat. Univ. Parma, Vol. 5, No. 1, 2014

Paolo Baroni [1]

Nonlinear parabolic equations with Morrey data

Pages: 65-92
Accepted: 30 July 2013
Mathematics Subject Classification (2010): 35R06, 35B65, 35K55.

Keywords: Calderón-Zygmund estimates, measure data problems, Morrey spaces.
[1] : Department of Mathematics, Uppsala Universitet, Lägerhyddsvägen 1, Uppsala, SE-751 06, Sweden

Abstract: 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.

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