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Том 216, № 2 (2016)
- Год: 2016
- Статей: 11
- URL: https://ogarev-online.ru/1072-3374/issue/view/14750
Article
Remark on the Hӧlder Continuity of p(x)-Harmonic Functions
Аннотация
We consider a p(x)-harmonic equation, where p(x) is measurable in Ω and is separated from 1 and infinity. It is shown that if p(x) is a radial function of x − x0, in a neighborhood of a point x0 ∈ Ω i.e., p(x) = p(|x − x0|) and p(t) is nonincreasing on (0, d), then p(x) is Hӧlder continuous at the point x0. Bibliography: 11 titles.
147-154
Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions in a System of Bodies with Piecewise Smooth Boundaries
Аннотация
We consider the boundary value problem for the radiative transfer equation with diffuse reflection and refraction conditions in a system of semitransparent bodies with piecewise smooth boundaries. For the problem with data in the complete scale of Lebesgue spaces we establish the existence and uniqueness of a solution. We obtain a priori estimates for the solution and show the continuous dependence of the solution on the data. The conjugate problem is also studied. Bibliography: 8 titles.
155-181
Error Estimates of Projection Type Methods for Solving Weakly Singular Integral Equations
Аннотация
We study projection type methods for numerical solution of one class of weakly singular integral Fredholm equations of the second kind including the integral radiative transfer equation. We consider Galerkin type methods and their modifications: the iterated Galerkin method (the Sloan method), the Kantorovich method, and the iterated Kantorovich method. For the approximating space we take the space of piecewise constant functions or the space of piecewise linear functions related to an arbitrary nonuniform grid. Error estimates are obtained.
182-218
Local Coarsening of Simplicial Subdivisions
Аннотация
We construct two types of simplicial subdivisions admitting an embedded local coarsening. In both cases, we propose coarsening algorithms and prove that the obtained simplicial subdivision is regular. For subdivisions of the second type we show that the local coarsening algorithm is recursive. Bibliography: 5 titles.
219-235
236-242
243-262
263-269
Inversion Formulas for Integral Operations of Weighted Plane Wave Type
Аннотация
We obtain the inversion formula for Newton B-potentials with Hӧlder densities. If the weight exponent is a natural number, the weighted plane waves are represented via spherical transformations of integral operations with plane waves. The inversion formulas for integral operations with kernel are presented by the action of the Poisson operator on some power of the inner product of vectors.
270-278
Asymptotic Analysis of an L-Shaped Junction of Two Elastic Beams
Аннотация
We propose a one-dimensional asymptotic model of an L-shaped junction of two thin two-dimensional elastic beams subject to boundary conditions of different type at external bean ends. The beams are described by standard systems of the Kirchhoff ordinary differential equations, whereas the transmission conditions on coincident (internal) nodes essentially depend on the type of boundary conditions on the external beam ends. The transmission conditions are obtained by analyzing the boundary layer near internal nodes. The asymptotics is justified with the help of a weighted anisotropic Korn inequality.
279-312
313-324
Error Estimates of Homogenization in the Neumann Boundary Problem for an Elliptic Equation with Multiscale Coefficients
Аннотация
We study the Neumann problem in a bounded domain Ω for a scalar elliptic equation with coefficients oscillating with respect to two groups of variables with periods of different smallness order. We prove the H1- and L2-estimates of homogenization. The estimates have the operator form and can be expressed in terms of the resolvent of the original problem and its approximations in the operator (L2(Ω)→H1(Ω))- and (L2(Ω)→L2(Ω))- norms.
325-344