Convex functionals and the stratification of the singular set of their stationary points
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DOI: 10.1016/j.aim.2018.08.008
Abstract: We prove partial regularity of stationary solutions and minimizers $u$ from a set $\Omega\subset \mathbb R^n$ to a Riemannian manifold $N$, for the functional $\int_\Omega F(x,u,|\nabla u|^2) dx$. The integrand $F$ is convex and satisfies… read more here.
Keywords: stratification; convex functionals; singular set; set stationary ... See more keywords
On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints
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DOI: 10.1109/tsp.2017.2788427
Abstract: The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions… read more here.
Keywords: optimality; probability distributions; convex functionals; functionals probability ... See more keywords
Refining and reversing the weighted arithmetic–geometric mean inequality involving convex functionals and application for the functional entropy
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DOI: 10.1186/s13660-020-02355-3
Abstract: In this paper, we present some refinements and reverses for some inequalities involving the weighted arithmetic mean and the weighted geometric mean of two convex functionals. Inequalities involving the Heinz functional mean are also obtained.… read more here.
Keywords: mean; entropy; convex functionals; weighted arithmetic ... See more keywords
The logarithmic mean of two convex functionals
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DOI: 10.1515/math-2020-0095
Abstract: Abstract The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well.… read more here.
Keywords: logarithmic mean; two convex; mean two; convex functionals ... See more keywords