We consider a class of non-uniformly nonlinear elliptic equations whose model is given by where p<q and a(x)â¥0, and establish the related nonlinear Caldeon-Zygmund theory. In particular, we provide sharp conditions under which the natural, and optimal, Calderon-Zygmund type result. holds for every Î³ â¥ 1 These problems naturally emerge as Euler-Lagrange equations of some variational integrals introduced and studied by Marcellini  and Zhikov  in the framework of Homogenisation and Lavrentiev phenomenon.
Calderón-Zygmund estimates and non-uniformly elliptic operators / Colombo, Maria; Mingione, Giuseppe. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 270:4(2016), pp. 1416-1478. [10.1016/j.jfa.2015.06.022]
Calderón-Zygmund estimates and non-uniformly elliptic operators
AbstractWe consider a class of non-uniformly nonlinear elliptic equations whose model is given by where p
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