Abstract
We study the first boundary value problem for the second-order fully nonlinear parabolic equation under natural structure conditions. The 1 , Q solution has a priori W1,0 infinite bound. And moreover we prove the esistence of viscosity solution by using the accretive operator. This is the extension of the method used in [ I ] . Our method has the advantage that the existence of solution does not depend on the esistence of super- and subsolutions such as perron's method. Finally the uniqueness of viscosity solution is proved by using the method developed in [2] and [3].
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