A dimension-free Hermite–Hadamard inequality via gradient estimates for the torsion function

Jianfeng Lu; Stefan Steinerberger

doi:10.1090/proc/14843

A dimension-free Hermite–Hadamard inequality via gradient estimates for the torsion function

Proceedings of the American Mathematical Society ◽

10.1090/proc/14843 ◽

2019 ◽

Vol 148 (2) ◽

pp. 673-679 ◽

Cited By ~ 2

Author(s):

Jianfeng Lu ◽

Stefan Steinerberger

Keyword(s):

Gradient Estimates ◽

Hadamard Inequality ◽

Torsion Function

Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2021.01.002 ◽

2021 ◽

Vol 147 ◽

pp. 60-97

Author(s):

Mathias Braun ◽

Karen Habermann ◽

Karl-Theodor Sturm

Keyword(s):

Optimal Transport ◽

Gradient Estimates

A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica ◽

10.1007/s10998-021-00425-7 ◽

2021 ◽

Author(s):

Milan Merkle ◽

Zoran D. Mitrović

Keyword(s):

Convex Functions ◽

Hadamard Inequality

Gradient estimates for divergence form parabolic systems from composite materials

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-01927-5 ◽

2021 ◽

Vol 60 (3) ◽

Author(s):

Hongjie Dong ◽

Longjuan Xu

Keyword(s):

Composite Materials ◽

Parabolic Systems ◽

Divergence Form ◽

Gradient Estimates

On a certain stability of the Hermite–Hadamard inequality

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0291 ◽

2008 ◽

Vol 465 (2102) ◽

pp. 571-583 ◽

Cited By ~ 5

Author(s):

Attila Házy ◽

Zsolt Páles

Keyword(s):

Functional Inequalities ◽

Hadamard Inequality ◽

Real Functions ◽

The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

Extensions of the Hermite–Hadamard inequality for harmonically convex functions via fractional integrals

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.06.051 ◽

2015 ◽

Vol 268 ◽

pp. 121-128 ◽

Cited By ~ 3

Author(s):

Feixiang Chen

Keyword(s):

Convex Functions ◽

Fractional Integrals ◽

Hadamard Inequality ◽

Harmonically Convex Functions

Gradient estimates for the heat kernels in higher dimensional Heisenberg groups

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-009-0198-y ◽

2010 ◽

Vol 31 (3) ◽

pp. 305-314 ◽

Cited By ~ 4

Author(s):

Bin Qian

Keyword(s):

Heat Kernels ◽

Gradient Estimates ◽

Heisenberg Groups ◽

Higher Dimensional

HARNACK-TYPE INEQUALITIES FOR THE POROUS MEDIUM EQUATION ON A MANIFOLD WITH NON-NEGATIVE RICCI CURVATURE

International Journal of Mathematics ◽

10.1142/s0129167x11007525 ◽

2012 ◽

Vol 23 (04) ◽

pp. 1250009 ◽

Cited By ~ 2

Author(s):

JEONGWOOK CHANG ◽

JINHO LEE

Keyword(s):

Porous Medium ◽

Riemannian Manifold ◽

Ricci Curvature ◽

Porous Medium Equation ◽

Complete Riemannian Manifold ◽

Gradient Estimates ◽

Medium Equation

We derive Harnack-type inequalities for non-negative solutions of the porous medium equation on a complete Riemannian manifold with non-negative Ricci curvature. Along with gradient estimates, reparametrization of a geodesic and time rescaling of a solution are key tools to get the results.

Gradient estimates for weighted harmonic function with Dirichlet boundary condition

Nonlinear Analysis ◽

10.1016/j.na.2021.112498 ◽

2021 ◽

Vol 213 ◽

pp. 112498

Author(s):

Nguyen Thac Dung ◽

Jia-Yong Wu

Keyword(s):

Boundary Condition ◽

Harmonic Function ◽

Dirichlet Boundary Condition ◽

Dirichlet Boundary ◽

Gradient Estimates

Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex

Journal of Inequalities and Applications ◽

10.1186/1029-242x-2012-247 ◽

2012 ◽

Vol 2012 (1) ◽

Cited By ~ 23

Author(s):

Ali Barani ◽

Amir G Ghazanfari ◽

Sever S Dragomir

Keyword(s):

Hadamard Inequality

Gradient estimates for semilinear elliptic systems and other related results

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210515000347 ◽

2015 ◽

Vol 145 (6) ◽

pp. 1313-1330 ◽

Cited By ~ 6

Author(s):

Panayotis Smyrnelis

Keyword(s):

Liouville Theorem ◽

Elliptic Systems ◽

Gradient Estimates ◽

Alternative Form ◽

Strong Monotonicity ◽

Energy Tensor ◽

Planar Domains ◽

Stress Energy ◽

General Phase ◽

Double Well Potential

A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville theorem for general phase transition potentials. Gradient estimates are also established for several kinds of elliptic systems. They allow us to prove the Liouville theorem in some particular cases. Finally, we give an alternative form of the stress–energy tensor for solutions defined in planar domains. As an application, we deduce a (strong) monotonicity formula.