Related papers: The linear constraints in Poincar\'{e} and Korn ty…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…
We introduce a quantitative version of Property A in order to estimate the L^p-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to…
We characterize complete RNP-differentiability spaces as those spaces which are rectifiable in terms of doubling metric measure spaces satisfying some local $(1, p)$-Poincar\'e inequalities. This gives a full characterization of spaces…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
We prove a new type of Poincar\'e inequality on abstract Wiener spaces for a family of probability measures which are absolutely continuous with respect to the reference Gaussian measure. This class of probability measures is characterized…
Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large…
We use the characterization of weak type inequalities via Garsia-Rodemich conditions to show self improving properties of Poincar\'e-Sobolev inequalities in a very general context.
We give bounds on the Poincare (inverse spectral gap) constant of a non-negative, integer-valued random variable W, under negative dependence assumptions such as ultra log-concavity and total negative dependence. We show that the bounds…
We establish a family of coercive Korn-type inequalities for generalised incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the…
This note is devoted to the proof of convex Sobolev (or generalized Poincar\'{e}) inequalities which interpolate between spectral gap (or Poincar\'{e}) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of…
Brascamp--Lieb-type, weighted Poincar\'{e}-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general $\kappa$-concave probability measures (in the hierarchy of convex measures). In analogy…
If Poincar{\'e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and…
The problem of characterizing weak limits of sequences of solutions for a non-linear diffusion equation of $p$-laplacian type is addressed. It is formulated in terms of certain moments of underlying Young measures associated with main…
It is shown that the $p$-Poincar\'e inequality holds on an open set $\Omega$ in $\mathbb{R}^n$ if and only if the strict $p$-capacitary inradius of $\Omega$ is finite. To that end, new upper and lower bounds for the infimum for the…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
For a bounded three-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically two kind of sensitivity indices are linked by a Poincar\'e type inequality, which…
In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincar\'e map is decomposed to the…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…