Asymptotics of the s - perimeter as s ↘ 0
نویسنده
چکیده
We deal with the asymptotic behavior of the s-perimeter of a set E inside a domain Ω as s ↘ 0. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of E and Ω. Moreover, we construct examples of sets for which the limit does not exist.
منابع مشابه
On the Asymptotics of the Finite-Perimeter Partition Function of Two-Dimensional Lattice Vesicles
We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q, in the inflated regime, q > 1. The approach q → 1+ of the asymptotic form is examined.
متن کاملAsymptotics of derivatives of orthogonal polynomials on the unit circle
We show that ratio asymptotics of orthogonal polynomials on the circle imply ratio asymptotics for all their derivatives. Moreover, by reworking ideas of P. Nevai, we show that uniform asymptotics for orthogonal polynomials on an arc of the unit circle imply asymptotics for all their derivatives. Let be a nite positive Borel measure on the unit circle (or [0; 2 ]). Let f'ng denote the orthonor...
متن کاملMean perimeter and mean area of the convex hull over planar random walks
We investigate the geometric properties of the convex hull over n successive positions of a planar random walk, with a symmetric continuous jump distribution. We derive the large n asymptotic behavior of the mean perimeter. In addition, we compute the mean area for the particular case of isotropic Gaussian jumps. While the leading terms of these asymptotics are universal, the subleading (correc...
متن کاملLarge Data Limit for a Phase Transition Model with the p-Laplacian on Point Clouds
The consistency of a nonlocal anisotropic Ginzburg-Landau type functional for data classification and clustering is studied. The Ginzburg-Landau objective functional combines a double well potential, that favours indicator valued function, and the p-Laplacian, that enforces regularity. Under appropriate scaling between the two terms minimisers exhibit a phase transition on the order of ε = εn w...
متن کاملShape Effects and Definition of Hydraulic Radius in Manning 's Equation in Open Channel Flow
In the Manning equation the hydraulic radius can be defined as the cross-section dimension of the shape. In pipe flow the bed shear stress is assumed to be uniformly distributed along the wetted perimeter which cannot be true in open channel flow. Hence, three approximation of the true boundary shear-stress distribution are examined and more practical conveyance depth or resistance radius formu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012