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

N. V. Krylov

doi:10.3934/cpaa.2018119

Article Contents

2018, Volume 17, Issue 6: 2495-2516. Doi: 10.3934/cpaa.2018119

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

N. V. Krylov

127 Vincent Hall, University of Minnesota, Minneapolis, MN, 55455

Received: September 30, 2017

Revised: January 31, 2018

Published: June 2018

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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.

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Mathematics Subject Classification: 35K55, 35B65.

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References

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