Published Paper
Inserted: 12 mar 2012
Last Updated: 20 mar 2014
Journal: Ann. Mat. Pura Appl.
Volume: 193
Number: 2
Pages: 325-358
Year: 2014
Links:
http://www.springerlink.com/content/h38513484j780hhu/
Abstract:
We deal with the solutions to nonlinear elliptic equations of the form $$-\textrm{div}\, a(x,Du)+g(x,u)=f,$$ with $f$ being just a summable function, under standard growth conditions on~$g$ and~$a$. We prove general local decay estimates for level sets of the gradient of solutions in turn implying very general estimates in rearrangement and non-rearrangement function spaces, up to Lorentz-Morrey spaces. The results obtained are in clear accordance with the classical Gagliardo-Nirenberg interpolation theory.
Keywords: Nonlinear elliptic problems, Lower order term, Morrey-Lorentz regularity, Rearrangement function spaces, Gagliardo-Nirenberg interpolation inequalities
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