Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 24, pp. 1-20.

Title: Existence results for boundary problems for uniformly
       elliptic and parabolic fully nonlinear equations

Authors: M. G. Crandall (Univ. of California, Santa Barbara, USA)
         M. Kocan       (Univ. of Cologne,Germany) 
         P. L. Lions    (Univ. Paris-Dauphine,France) 
         A. Swiech      (Georgia Inst. of Technology, Atlanta, USA)

Abstract: 
We study existence of continuous weak (viscosity) solutions of
Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly 
elliptic and parabolic equations. Two types of results are obtained in
contexts where uniqueness of solutions fails or is unknown.
For equations with merely measurable coefficients we prove 
solvability of the problem, while in the continuous 
case we construct maximal and minimal solutions. Necessary
barriers on external cones are also constructed.
 

Submitted May 20, 1999. Published July 1, 1999.
Math Subject Classification: 35J25, 35J60, 35J65, 35K20, 35K55, 35K60, 49L25.
Key Words: Uniformly elliptic and parabolic equations; viscosity solutions; 
           good solutions; exterior cone condition; barrier functions.