Related papers: Stability for the logarithmic Sobolev inequality

We provide a proof of the sharp log-Sobolev inequality on a compact interval.

In the framework of variable exponent Sobolev spaces, we prove that the variational eigenvalues defined by inf sup procedures of Rayleigh ratios for the Luxemburg norms are all stable under uniform convergence of the exponents.

In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases.…

We prove a quantitative stability result for the Heisenberg-Pauli-Weyl inequality. This yields next and next-to-next order correction terms, sharpening the inequality in all dimensions.

In this article, we study the increasing stability property for the determination of the potential in the Schr\"odinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat and homogeneous boundary…

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

The interest of the scientific community for the existence, uniqueness and stability of solutions to PDE's is testified by the numerous works available in the literature. In particular, in some recent publications on the subject an…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

The stability issue of generalized modified gravitational models is discussed with particular emphasis to de Sitter solutions. Two approaches are briefly presented.

In this paper, we obtain a sharp Garliardo-Nirenberg inequality on integer lattices and characterize its rigidity. Moreover, as a consequence of the sharp Garliardo-Nirenberg inequality, we obtain sharp logarithmic Sobolev inequalities on…

We prove logarithmic conditional stability up to the final time for backward-parabolic operators whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. The result complements previous achievements of Del…

Using a dimension reduction argument and a stability version of the weighted Sobolev inequality on half space recently proved by Seuffert, we establish, in this paper, some stability estimates (or quantitative estimates) for a family of the…

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also…

This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property,…

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$, while it…

In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…

We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous…

We prove a stability version of the isodiametric inequality on the sphere and in the hyperbolic space.

We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based…