Calculus of Variations and Geometric Measure Theory

A. Di Castro - G. Palatucci

Measure data problems, lower order terms and interpolation effects

created by palatucci on 12 Mar 2012
modified on 20 Mar 2014


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


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