Quadratic growth of solutions of fully nonlinear second order equations in Rn

Abstract

Fully nonlinear (degenerate) elliptic and parabolic equations of second order in RN of the forms u + F(D2u) = f(x) and Ut + F(D2u) = 0, where F is a nonincreasing function from the symmetric N x N matrices equipped with their usual ordering to R, are considered. Existence and uniqueness theorems are proved in the class of solutions of quadratic growth when the data (f in the elliptic case and the initial data in the parabolic case) have suitable properties. In the parabolic case, a semiflow is obtained and the "inverse problem" of determining properties of similar flows necessary and sufficient to guarantee that they are the time t maps for such an equation is solved. © 1990, Khayyam Publishing. All rights reserved.