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Elliptic Boundary Value Problems in Domains with Point Singularities
Introduction Part 1: Boundary value problems for ordinary differential equations on the half-axis Elliptic boundary value problems in the half-space Elliptic boundary value problems in smooth domains
On the Bourgain, Brezis, and Mironescu Theorem Concerning Limiting Embeddings of Fractional Sobolev Spaces
The article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: Ws,p ? Lpn/(n-sp) as s ? 1 and s ? n/p. Thei
Sobolev Spaces: with Applications to Elliptic Partial Differential Equations
Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable
Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations
Introduction Singularities of solutions to equations of mathematical physics: Prerequisites on operator pencils Angle and conic singularities of harmonic functions The Dirichlet problem for the Lame
Linear Water Waves: A Mathematical Approach
Preface Part I. Time-Harmonic Waves: 1. Green's functions 2. Submerged obstacles 3. Semisubmerged bodies, I 4. Semisubmerged bodies, II 5. Horizontally-periodic trapped waves Part II. Ship Waves on
Theory of multipliers in spaces of differentiable functions
CONTENTS Introduction Chapter I. Embedding theorems for Sobolev spaces § 1.1. The summability with respect to a measure of functions from the spaces and , § 1.2. The summability with respect to a
Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains
A mixed boundary value problem for the Stokes system in a polyhedral domain is considered. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescr
ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLES
Complete asymptotic expansions are found for the first eigenvalues and eigenfunctions of classical problems for the Laplace operator in two- and three-dimensional domains with small holes.
On approximate approximations using Gaussian kernels
This paper discusses quasi-interpolation and interpolation with Gaussians. Estimates are obtained showing a high-order approximation up to some saturation error negligible in numerical applications.
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