Uniqueness for $L_p$-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms

Abstract

In this article we present several results concerning uniqueness of $C$-viscosity and $L_p$-viscosity solutions for fully nonlinear parabolic equations. In case of the Isaacs equations we allow lower order terms to have just measurable bounded coefficients. Higher-order coefficients are assumed to be Hölder continuous in $x$ with exponent slightly less than $1/2$. This case is treated by using stability of maximal and minimal $L_p$-viscosity solutions.

27 p, a few inconsistencies are corrected

References in corpus (1)

• On the existence of $W_p^{1,2}$ solutions for fully nonlinear parabolic equations under either relaxed or no convexity assumptions