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The Poincaré Inequality for 3D-Vector Fields and the Neumann Problem
For 3D-vector fields we obtain a family of integral inequalities that can be regarded as the Poincaré inequality within the framework of field...
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Poincaré Inequality and Topological Rigidity of Translators and Self-Expanders for the Mean Curvature Flow
We prove an abstract structure theorem for weighted manifolds supporting a weighted f -Poincaré inequality and whose ends satisfy a suitable...
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A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincaré Boundary Conditions
AbstractFor a certain class of second-order hyperbolic systems, a mixed problem with Dirichlet and Poincaré boundary conditions is studied. In the...
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Hardy–Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
We prove a family of Hardy–Rellich and Poincaré identities and inequalities on the hyperbolic space having, as particular cases, improved...
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Non-degeneracy of Poincaré–Einstein Four-Manifolds Satisfying a Chiral Curvature Inequality
A Poincaré–Einstein metric g is called non-degenerate if there are no non-zero infinitesimal Einstein deformations of g , in Bianchi gauge, that lie...
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From the Brunn-Minkowski Inequality to a Class of Generalized Poincaré-Type Inequalities for Torsional Rigidity
In this paper, we establish a class of generalized Poincaré-type inequalities for torsional rigidity on the boundary of a convex body of class
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Poincaré inequalities on graphs
Every graph of bounded degree endowed with the counting measure satisfies a local version of L p -Poincaré inequality, p ∈ [1, ∞]. We show that on...
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Second Order Spherical Concentration
In this chapter we discuss natural conditions imposed on the functions f on the unit sphere which guarantee smaller deviations of f from their means...
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Rigidity of Complete Manifolds with Weighted Poincaré Inequality
We consider complete Riemannian manifolds which satisfy a weighted Poincarè inequality and have the Ricci curvature bounded below in terms of the...
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Poincaré and Logarithmic Sobolev Inequalities for Nearly Radial Measures
Poincaré inequality has been studied by Bobkov for radial measures, but few are known about the logarithmic Sobolev inequality in the radial case. We...
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A pointwise differential inequality and second-order regularity for nonlinear elliptic systems
A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a...
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Remarks about the mean value property and some weighted Poincaré-type inequalities
We start providing a quantitative stability theorem for the rigidity of an overdetermined problem involving harmonic functions in a punctured domain....
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Eigenvalue Problems of Second Order Linear Elliptic Operators
Eigenvalue problems have a wide range of applications. In particular, the existence of positive solutions to second order semi-linear and...
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Properties of the Affine Poincaré Wavelet Transform
The affine Poincaré wavelet transform is the convolution of the analyzed function and the parameter-dependent function called a wavelet. The wavelet...
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Harnack Inequality and the Relevant Theorems on Finsler Metric Measure Manifolds
In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler...
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Second-Order Bounds on Correlations Between Increasing Families
Harris’s correlation inequality states that any two monotone functions on the Boolean hy-percube are positively correlated. Talagrand [11] started a...
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Decay Rate of the Eigenvalues of the Neumann-Poincaré Operator
If the boundary of a domain in three dimensions is smooth enough, then the decay rate of the eigenvalues of the Neumann-Poincaré operator is known...
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Periodic Solutions of a Second Order Discontinuous Nonautonomous Differential Equation
In this paper, we are concerned with a problem of periodic solution for a second order nonautonomous differential equation with a discontinuity line....