Selçuk Journal
of
Applied Mathematics
WinterSpring,
2002
Volume 3
Number 1
Research Center
of
Applied Mathematics

SJAM
WinterSpring 2002, Volume 3  Number 1

Good solutions of fully nonlinear parabolic equations 
Tran Duc Van^{1}
, Tran Van Bang^{2} 
^{1 }
Hanoi Institute of Mathematics, P.O. Box 631 Bo
Ho, 10.000 Hanoi, Vietnam;
email:
tdvan@thevinh.ncst.ac.vn
^{2 }
Hanoi Pedagogical University, Xuan hoa, Hanoi,
Vietnam;
Received: April 02, 2002

Summary
In this paper, we introduce the notion
of a "good" solution of a fully nonlinear parabolic equation and
show that "good" solutions are equivalent to L^{p}
viscosity solutions of such equations. The results here generalize
the ones in [8] about "good" solutions of fully nonlinear elliptic
equations. We give here an explicit construction of parabolic
equations with L^{p} strong solutions that
approximate some nonlinear parabolic equation and its L^{p}
viscosity solution. 

Key
words
SJAM
SummerAutumn 2002, Volume 3  Number 1 
Good solutions of
fully nonlinear parabolic equations 
Tran Duc Van^{1}
, Tran Van Bang^{2} 
^{1 }
Hanoi Institute of Mathematics, P.O. Box 631
Bo Ho, 10.000 Hanoi, Vietnam;
email:
tdvan@thevinh.ncst.ac.vn
^{2 }
Hanoi Pedagogical University, Xuan hoa,
Hanoi, Vietnam;
Received: April 02, 2002

Summary
In this paper, we introduce the
notion of a "good" solution of a fully nonlinear parabolic
equation and show that "good" solutions are equivalent to L^{p}
viscosity solutions of such equations. The results here
generalize the ones in [8] about "good" solutions of fully
nonlinear elliptic equations. We give here an explicit
construction of parabolic equations with L^{p}
strong solutions that approximate some nonlinear parabolic
equation and its L^{p} viscosity solution. 

Key words
L^{p}viscosity
solutions, good solutions, strong solutions, fully nonlinear
parabolic equations 

Mathematics Subject
Classification (1991): 35J60, 35J65,
49L25
*
This research was supported in part by National Council on Natural
Science, Vietnam.

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