相关论文: Corrigendum for the comparison theorem in "A new d…
The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main…
This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous…
This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three…
In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Renyi's…
A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.
Aleksandrov-Bakelman-Pucci maximum principles are studied for a class of fully nonlinear integro-differential equations of order $\sigma\in [2-\varepsilon_0,2)$, where $\varepsilon_0$ is a small constant depending only on given parameters.…
In this paper we solve a problem raised by Guti\'errez and Montanari about comparison principles for $H-$convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal…
We establish the general form of a geometric comparison principle for $n$-fold convolutions of certain singular measures in $\mathbb{R}^d$ which holds for arbitrary $n$ and $d$. This translates into a pointwise inequality between the…
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of…
We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over…
Convexity is a key concept in information theory, namely via the many implications of Jensen's inequality, such as the non-negativity of the Kullback-Leibler divergence (KLD). Jensen's inequality also underlies the concept of Jensen-Shannon…
We derive a number of sharp upper bounds for the deficit in the Alexandrov-Fenchel inequality using a weighted Minkowski integral formula and an integral formula for the deficit in Jensen's inequality. Our estimates yield results under…
We prove a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the $p-$Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no…
In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations, the proof of which relies on an appropriate generalization of the convex envelope to a…
In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is established that…
In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.
In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.
We extend Dragomir's refinement of Jensen's inequality from the dicrete to the general case, identifying the equality conditions.
This paper establishes a converse comparison theorem for real-valued decoupled forward backward stochastic differential equations with jumps.