Related papers: Asymptotics of the conformal modulus of a nonsymme…
In this work, we study the distortion of the exterior conformal modulus of a symmetric quadrilateral, when stretched in the direction of the abscissa axis with the coefficient $H\to \infty$. By using some facts from the theory of elliptic…
We investigate asymptotical behavior of the conformal module of a doubly-connected domain which is the difference of two homothetic rectangles under stretching it along the abscissa axis. Thereby, we give the answer to a question put by…
In this paper, we focus on studying the distortion of the exterior conformal modulus of a quadrilateral of sufficiently arbitrary form under the stretching map along the abscissa axis with coefficient $H\to\infty$. By using the properties…
We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g.,…
We prove that if $\Omega$ is a simply connected quadrature domain for a distribution with compact support and the infinity point belongs the boundary, then the boundary has an asymptotic curve that is either a straight line or a parabola or…
The aim of this article is to analyze the asymptotic behaviour of the eigenvalues of elliptic operators in divergence form with mixed boundary type conditions for domains that become unbounded in several directions, while they stay bounded…
We extend and simplify results of \cite{Din~2009} where the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric in annuli is studied. Similarly as in \cite{Din~2009} the description enables us to construct an…
The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…
In this paper, the asymptotic behavior of the solutions of a monotone problem posed in a locally periodic oscillating domain is studied. Nonlinear monotone boundary conditions are imposed on the oscillating part of the boundary whereas the…
We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries…
This paper investigates the asymptotic boundary behavior of the holomorphic bisectional curvature for weighted Bergman metrics. By characterizing extremal functions via $L^2$-orthogonal projections, we establish an explicit formula for the…
We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem…
We consider the Vlasov--Poisson system in a $C^3$ convex domain $D$ with a perfectly conducting wall. We introduce the asymptotic domain $D_{\infty}$ for the domain $D$. Then under acceptable assumptions on $D$, we show that for localized…
The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the…
We prove three theorems about the asymptotic behavior of solutions $u$ to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, under very mild hypotheses, we show that the doubling index…
We derive an asymptotic expansion for two-dimensional displacement field associated to thin elastic inhomogeneities having no uniform thickness. Our derivation is rigorous and based on layer potential techniques. We extend these techniques…
The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic…
In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment…
Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…