DOI: 10.68381/jca20048 ISSN: 0944-6532
Fractional Regularity for Nonlinear Elliptic Problems with Measure Data
Agnese Di Castro, Giampiero Palatucci
We consider nonlinear elliptic equations of the type
-\text{\rm div}\,a(x, Du)=\mu
−
div
a
(
x
,
D
u
)
=
μ
having a Radon measure on the right-hand side and prove fractional differentiability results of Calderón-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione [“The Calderón-Zygmund theory for elliptic problems with measure data”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6 (2007) 195–261], in turn improving a regularity result by G. R. Cirmi and S. Leonardi [“Higher differentiability for solutions of linear elliptic systems with measure data”, Discrete Contin. Dyn. Syst. 26 (2010) 89–104].