Related papers: Weak UCP and perturbed monopole equations

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to self-adjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be…

The purpose of this paper is to characterize weak supercyclicity for Hilbert-space contractions, which is shown to be equivalent to characterizing weak supercyclicity for unitary operators$.$ This is naturally motivated by an open question…

We prove strong unique continuation property for the differential inequality $|(\partial_t +\Delta)u(x,t)|\le V(x,t)|u(x,t)|$ with $V$ contained in weak spaces. In particular, we establish the strong unique continuation property for $V\in…

We study functions of least gradient as well as related superminimizers and solutions of obstacle problems in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show a standard weak Harnack…

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are…

We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an…

We prove some uniqueness results for weak solutions to some classes of parabolic Dirichlet problems.

We study the discrete eigenvalues emerging from the threshold of the essential spectrum of one or two-dimensional Schr\"odinger operators with complex-valued $ L^p $-potentials in a weak coupling regime. We derive necessary and sufficient…

We study the regularity of weak solutions to evolution equations with distributed order fractional time derivative. We prove a weak Harnack inequality for nonnegative weak supersolutions and H\"older continuity of weak solutions to this…

This paper is a follow up to an article by two of the authors dedicated to the study of Poincar\'e and logarithmic Sobolev inequalities for measures of the form $d\mu = e^{-U} d\nu$ where $e^{-U}$ is seen as a perturbation of $d\nu$.…

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic,…

This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces.…

We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$.…

We prove a unique continuation result for an ill-posed characteristic problem. A model problem of this type occurs in A.D.~Ionescu \& S.~Klainerman article (Theorem 1.1 in \cite{MR2470908}) and we extend their model-result using only…

We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation…

We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

A theorem is proved on the uniform estimation of the residual term of the asymptotic expansion with respect to a small parameter of the solution of the initial problem for a singularly perturbed differential operator weakly nonlinear…

Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.