منابع مشابه
THE k-HESSIAN EQUATION
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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In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k = 1, 2, · · · , n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect ...
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A Dirichlet problem for orthogonal Hessians in two dimensions is explicitly solved, by characterizing all piecewise C functions u : Ω ⊂ R → R with orthogonal Hessian in terms of a property named “second order angle condition” as in (1).
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In our previous paper on this topic, we introduced the notion of k-Hessian measure associated with a continuous k-convex function in a domain Ω in Euclidean n-space, k = 1, · · · , n, and proved a weak continuity result with respect to local uniform convergence. In this paper, we consider k-convex functions, not necessarily continuous, and prove the weak continuity of the associated k-Hessian m...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2020
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnaa288