Journal ArticleDOI
Capacitary functions in convex rings
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1977-09-01. It has received 203 citations till now.read more
Citations
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On the Hessian matrix and Minkowski addition of quasiconvex functions
Marco Longinetti,Paolo Salani +1 more
TL;DR: In this article, the class Q of quasiconvex functions with convex sublevel sets was studied, and the Minkowski addition of these functions was investigated in terms of the support function of the sublevel set.
Posted Content
The Brunn-Minkowski inequality and A Minkowski problem for nonlinear capacity
TL;DR: This article studies two classical potential-theoretic problems in convex geometry and an inequality of Brunn-Minkowski type for a nonlinear capacity in Laplace equation and its solutions in an open set.
Journal ArticleDOI
The p -capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems
Han Hong,Deping Ye,Ning Zhang +2 more
TL;DR: In this paper, the p-capacitary Orlicz-Brunn-Minkowski theory was proposed and solved under some mild conditions on the involving functions and measures.
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On the strict concavity of the harmonic radius in dimension N⩾3
TL;DR: In this paper, a result on the strict concavity of the harmonic radius in open convex domains of R N, for N⩾3, is given, which implies the strict convexity of Robin function and the uniqueness of harmonic center.
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Smoothness of certain degenerate elliptic equations
TL;DR: In this paper, it was shown that if u is nonconstant and real analytic in D, then the gradient of u does not vanish in D. Theorem 1 is false when p = 2.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.