We consider nonlinear elliptic equations of the type $$-\text{\rm div}\,a(x, Du)=\mu$$ having a Radon measure on the right-hand side and prove fractional differentiability results of Calder\'on-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione (Ann. Scu. Norm. Sup., 2007), in turn improving a regularity result by Cirmi \& Leonardi (DCDS-A, 2010).
Fractional Regularity for Nonlinear Elliptic Problems with Measure Data / Agnese Di, Castro; Palatucci, Giampiero. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 20:4(2013), pp. 901-918.
Fractional Regularity for Nonlinear Elliptic Problems with Measure Data
PALATUCCI, Giampiero
2013-01-01
Abstract
We consider nonlinear elliptic equations of the type $$-\text{\rm div}\,a(x, Du)=\mu$$ having a Radon measure on the right-hand side and prove fractional differentiability results of Calder\'on-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione (Ann. Scu. Norm. Sup., 2007), in turn improving a regularity result by Cirmi \& Leonardi (DCDS-A, 2010).File in questo prodotto:
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