Related papers: Asymptotic Plateau Problem
We study the symmetry properties of the weak positive solutions to a class of quasi-linear elliptic problems having a variational structure. On this basis, the asymptotic behaviour of global solutions of the corresponding parabolic…
The purpose of this article is to give a streamlined and self-contained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest…
We investigate the existence of non-constant uniformly-bounded minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic group. We show that whenever the Laplace term in the Allen-Cahn equation is small enough, there exist minimal…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
The problem of state estimation has a long history with many successful algorithms that allow analytical derivation or approximation of posterior filtering distribution given the noisy observations. This report tries to conclude previous…
The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal…
We study, via multiscale analysis, some defect of compactness phenomena which occur in bosonic and fermionic quantum mean-field problems. The approach relies on a combination of mean-field asymptotics and second microlocalized semiclassical…
In this paper we consider the initial value problem for a family of shallow water equations on the line $\R$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as…
Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.
We develop an approach to scattering theory for generalized $N$-body systems. In particular we consider a general class of three quasi-particle systems, for which we prove Asymptotic Completeness.
The convergence of polyhomogeneous expansions of zero-rest-mass fields in asymptotically flat spacetimes is discussed. An existence proof for the asymptotic characteristic initial value problem for a zero-rest-mass field with…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
In this paper we provide an overview of important research works on response-adaptive randomization completed in the past decades.
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
We give a fairly complete solution to the asymptotic Plateau Problem for minimal surfaces in H^2xR. In particular, we identify the collection of finite Jordan curves in the asymptotic cylinder which bounds a minimal surface in H^2xR.
We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior…
In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to…
In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…