We deal with the solutions to nonlinear elliptic equations of the form $$ −div a(x,Du)+g(x,u)=f, $$ 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.
Measure data problems, lower-order terms and interpolation effects / Agnese Di Castro; Giampiero Palatucci. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 193:2(2014), pp. 325-358. [10.1007/s10231-012-0277-7]