SJAM Winter-Spring 2002, Volume 3 - Number 1

Tran Duc Van¹ , Tran Van Bang²

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 Summer-Autumn 2002, Volume 3 - Number 1

Good solutions of fully nonlinear parabolic equations

Tran Duc Van1 , Tran Van Bang2

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 Lp -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 Lp –strong solutions that approximate some nonlinear parabolic equation and its Lp -viscosity solution.

Key words Lp-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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