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Good Solutions of Fully Nonlinear Parabolic Equations

Author(s): Tran Duc Van | Tran Van Bang

Journal: Selçuk Journal of Applied Mathematics ISSN 1302-7980
Volume: 3; Issue: 1; Start page: 100; Date: 2002;
Original page

Keywords: L^{p}-viscosity solutions | good solutions | strong solutions | fully nonlinear parabolic equations.

ABSTRACT
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.