Hessian measures I
نویسندگان
چکیده
منابع مشابه
Hessian Measures Iii
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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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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This paper originates from the investigation of support measures of convex bodies (sets of positive reach), which form a central subject in convex geometry and also represent an important tool in related fields. We show that these measures are absolutely continuous with respect to Hausdorff measures of appropriate dimensions, and we determine the Radon-Nikodym derivatives explicitly on sets of ...
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ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 1997
ISSN: 1230-3429
DOI: 10.12775/tmna.1997.030