On the comparison principle for second order elliptic equations without first and zeroth order terms

Abstract

We consider the comparison principle for semicontinuous viscosity sub- and supersolutions of second order elliptic equations on the form $F(D^{2}w,x)=0$. A structural condition on the operator is presented that seems to unify the different existing theories. A new result is obtained and the proofs of the classical results are simplified.

arXiv comment36 pages, 5 figures