On the exterior problem for parabolic k-Hessian equations
نویسندگان
چکیده
<p style='text-indent:20px;'>We use Perron method to prove the existence of ancient solutions exterior problem for parabolic k-Hessian equations <inline-formula><tex-math id="M1">\begin{document}$ -u_tS_k(D^2u) = 1 $\end{document}</tex-math></inline-formula> with prescribed asymptotic behavior at infinity.</p>
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The k-Hessian is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equations. It is elliptic when restricted to k-admissible functions. In this paper we establish the existence and regularity of k-admissible solutions to the Dirichlet problem of the k-Hessian equation. By a g...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2022
ISSN: ['1534-0392', '1553-5258']
DOI: https://doi.org/10.3934/cpaa.2022106