CPAA
Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations
Limei Dai
Communications on Pure & Applied Analysis 2011, 10(6): 1707-1714 doi: 10.3934/cpaa.2011.10.1707
In this paper, we use the Perron method to prove the existence of viscosity solutions with asymptotic behavior at infinity to fully nonlinear uniformly elliptic equations in $R^n$.
keywords: entire solutions asymptotic behavior. Fully nonlinear uniformly elliptic equations
CPAA
Multi-valued solutions to a class of parabolic Monge-Ampère equations
Limei Dai
Communications on Pure & Applied Analysis 2014, 13(3): 1061-1074 doi: 10.3934/cpaa.2014.13.1061
In this paper, we investigate the multi-valued solutions of a class of parabolic Monge-Ampère equation $-u_{t}\det(D^{2}u)=f$. Using the Perron method, we obtain the existence of finitely valued and infinitely valued solutions to the parabolic Monge-Ampère equations. We generalize the results of elliptic Monge-Ampère equations and Hessian equations.
keywords: Perron method multi-valued solutions Parabolic Monge-Ampère equations viscosity solutions existence.

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