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

N. V. Krylov

doi:10.3934/cpaa.2018119

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

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this article we present several results concerning uniqueness of C-viscosity and Lp-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 Lp-viscosity solutions.

Original language	English (US)
Pages (from-to)	2495-2516
Number of pages	22
Journal	Communications on Pure and Applied Analysis
Volume	17
Issue number	6
DOIs	https://doi.org/10.3934/cpaa.2018119
State	Published - Nov 2018

Bibliographical note

Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.

Keywords

Fully nonlinear equations
Isaacs equations
Viscosity solutions

Publisher link

10.3934/cpaa.2018119

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abstract = "In this article we present several results concerning uniqueness of C-viscosity and Lp-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 H{\"o}lder continuous in x with exponent slightly less than 1/2. This case is treated by using stability of maximal and minimal Lp-viscosity solutions.",

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N2 - In this article we present several results concerning uniqueness of C-viscosity and Lp-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 Lp-viscosity solutions.

AB - In this article we present several results concerning uniqueness of C-viscosity and Lp-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 Lp-viscosity solutions.

KW - Fully nonlinear equations

KW - Isaacs equations

KW - Viscosity solutions

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