Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule

摘要

A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x, u, Du, D(2)u) = 0 is under consideration. (c) 2005 Elsevier Inc. All rights reserved.