Related papers: Logarithmic stability estimates for initial data i…

We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

Let (H_t) be the Ornstein-Uhlenbeck semigroup on R^d with covariance matrix I and drift matrix \lambda(R-I), where \lambda>0 and R is a skew-adjoint matrix and denote by \gamma_\infty the invariant measure for (H_t). Semigroups of this form…

We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\mathbb R}^d;{\mathbb R}^m)$, $(d,m \ge 1)$ with $p\in [1,+\infty)$. Sufficient conditions for the associated evolution operator ${\bf…

We identify sharp spaces and prove quantitative and non-quantitative stability results for the logarithmic Sobolev inequality involving Wasserstein and $L^p$ metrics. The techniques are based on optimal transport theory and Fourier…

We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are defined. These estimates are expressed in…

We prove that a probability solution of the stationary Kolmogorov equation generated by a first order perturbation $v$ of the Ornstein--Uhlenbeck operator $L$ possesses a highly integrable density with respect to the Gaussian measure…

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck…

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…

Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…

We consider a generic modified logarithmic Sobolev inequality (mLSI) of the form $\mathrm{Ent}_{\mu}(e^f) \le \tfrac{\rho}{2} \mathbb{E}_\mu e^f \Gamma(f)^2$ for some difference operator $\Gamma$, and show how it implies two-level…

We study a generalized curvature dimension inequality which is suitable for subelliptic Ornstein-Uhlenbeck type operators and deduce convergence to equilibrium in the $L^2$ and entropic sense. The main difficulty is that the operators we…

These Notes are intended for graduate or undergraduate students who have familiarity with Lebesgue measure theory, partial differential equations, and functional analysis. The main topics covered in this work are the study of the Cauchy…

Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…

In this note we consider the stability of posterior measures occuring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function. This extends the well-posedness analysis of Bayesian inverse problems. In…

We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint…

In this paper, we prove that the first (positive) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator \[ L(u)=\Delta u-(\nabla u,x), \] is strongly log-concave if the domain is bounded and convex, which improves the conclusion in [6].…

Motivated by Talagrand's conjecture on regularization properties of the natural semigroup on the Boolean hypercube, and in particular its continuous analogue involving regularization properties of the Ornstein-Uhlenbeck semigroup acting on…

This paper aims to investigate a full numerical approximation of non-autonomous semilnear parabolic partial differential equations (PDEs) with nonsmooth initial data. Our main interest is on such PDEs where the nonlinear part is stronger…

We consider a second-order parabolic equation in $\bR^{d+1}$ with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally H\"older continuous in the space variables.…