Alberto Farina, Enrico Valdinoci
Pointwise estimates and rigidity results 
for possibly singular and degenerate elliptic PDEs 
with general nonlinearities
(192K, pdf)

ABSTRACT.  We prove pointwise gradient bounds 
for entire solutions of PDEs of the form 
$$ {\mathcal{L}} u(x)=\psi(x,u(x),
abla u(x)),$$ 
where ${\mathcal{L}}$ is an elliptic operator (possibly 
singular or degenerate). 
Thus, we obtain some Liouville type 
rigidity results. Some classical results of J.~Serrin 
are also recovered as particular cases of our approach.