Related papers: Interpolation inequalities in pattern formation
We consider a one-dimensional version of a variational model for pattern formation in biological membranes. The driving term in the energy is a coupling between the order parameter and the local curvature of the membrane. We derive scaling…
Using factorisation and Arov-Krein inequality results, we derive important inequalities (in terms of $S$-nodes) in interpolation problems.
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
Interpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
We prove an endpoint version of the uniform Sobolev inequalities in Kenig-Ruiz-Sogge [8]. It was known that strong type inequalities no longer hold at the endpoints; however, we show that restricted weak type inequalities hold there, which…
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…
This expository thesis contains a study of four interpolation theorems, the requisite background material, and a few applications. The materials introduced in the first three sections of Chapter 1 are used to motivate and prove the…
We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new…
Interpolation inequalities play an important role in the study of PDEs and their applications. There are still some interesting open questions and problems that related to integral estimates and regularity of solutions to the elliptic…
We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
In this article, a proof of the interpolation inequality along geodesics in $p$-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel-Brascamp-Lieb inequality for general Riemannian and…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…