Geodesic
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations
Electronic journal of differential equations, Tome 1999 (1999)
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.
Classification : 35J25, 35J60, 35J65, 35K20, 35K55, 35K60, 49L25
Keywords: uniformly elliptic and parabolic equations, viscosity solutions, good solutions, exterior cone condition, barrier functions 
@article{EJDE_1999__1999__a130,
     author = {Crandall,  M.G. and Kocan,  M. and Lions,  P.L. and \'Swi\c{e}ch,  A.},
     title = {Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0927.35029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a130/}
}
TY  - JOUR
AU  - Crandall,  M.G.
AU  - Kocan,  M.
AU  - Lions,  P.L.
AU  - Świȩch,  A.
TI  - Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations
JO  - Electronic journal of differential equations
PY  - 1999
VL  - 1999
UR  - http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a130/
LA  - en
ID  - EJDE_1999__1999__a130
ER  - 
%0 Journal Article
%A Crandall,  M.G.
%A Kocan,  M.
%A Lions,  P.L.
%A Świȩch,  A.
%T Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations
%J Electronic journal of differential equations
%D 1999
%V 1999
%U http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a130/
%G en
%F EJDE_1999__1999__a130
Crandall,  M.G.; Kocan,  M.; Lions,  P.L.; Świȩch,  A. Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a130/