Good Solutions of Fully Nonlinear Parabolic Equations

Tran Duc Van, Tran Van Bang

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.

Keywords


L^{p}-viscosity solutions; good solutions; strong solutions; fully nonlinear parabolic equations.

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