Positivity Cases, Estimates and Asymptotic Expansions for Condenser Capacities
نویسنده
چکیده
We study positivity cases, estimates and asymptotic expansions of condenser p-capacities of points and segments in a given bounded domain, having in mind application fields, such as imaging, requiring detection and quantification of zero measure sets. We first establish estimates of capacities when the internal part of the condenser has a non-empty interior. The study of the point and its approximation by balls of small radiuses follow. Our main contribution is then to introduce equidistant condensers and to establish the positivity cases of d-dimensional condenser capacities of segments in a new way bringing out the relationship with the d-dimensional and more significantly with the (d− 1)-dimensional condenser capacities of points. We discuss how equidistant condensers might allow to obtain by induction the posivity cases for compact submanifolds of higher dimensions. For estimation purposes, we then introduce elliptical condensers and provide an estimate and the asymptotic expansion for the condenser capacity of a segment in the harmonic case p = 2. 1. Condenser capacities 1.
منابع مشابه
Estimates and asymptotic expansions for condenser p-capacities. The anisotropic case of segments
We provide estimates and asymptotic expansions of condenser p-capacities and focus on the anisotropic case of segments. After preliminary results, we study p-capacities of points with respect to asymptotic approximations, positivity cases and convergence speed of descending continuity. We introduce equidistant condensers to point out that the anisotropy caused by a segment in the p-Laplace equa...
متن کاملSecond Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum
This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright} where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...
متن کاملAsymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملFreezing in a Finite Slab Using Extensive Perturbation Expansions Method
In this paper Mathematica is used to solve the moving boundary problem of freezing in a finite slab for higher order perturbations. Mathematica is a new system which makes it possible to do algebra with computer. More specifically, it enables researchers to find the location of the ice at any time for as high order of perturbation as one whishes. Using of Mathematica and outer solution and an i...
متن کاملDecay estimates of solutions to the IBq equation
In this paper we focus on the Cauchy problem for the generalized IBq equation with damped term in $n$-dimensional space. We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value, provided that the initial value is suitably small. Moreover, we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...
متن کامل