Related papers: Analytic and Gevrey class regularity for parametri…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
In this paper we study the weighted Gevrey class regularity of Euler equation in the whole space R 3. We first establish the local existence of Euler equation in weighted Sobolev space, then obtain the weighted Gevrey regularity of Euler…
Given any elliptic system with $t$-independent coefficients in the upper-half space, we obtain representation and trace for the conormal gradient of solutions in the natural classes for the boundary value problems of Dirichlet and Neumann…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the…
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on a scalar parameter.…
In this paper, we study the first eigenvalue of a nonlinear elliptic system involving $p$-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…
In this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population…
In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence rate of the quasi-Monte Carlo method for approximation of the…
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…
We consider the initial value problem (IVP) associated to a fifth order KdV-BBM type model that describes the propagation of unidirectional water waves. We prove that the regularity in the initial data propagates in the solution, in other…
We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the…
In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
We show that the solutions of SG elliptic boundary value problems defined on the complement of compact sets or on the half-space have some regularity in Gelfand-Shilov spaces. The results are obtained using classical results about Gevrey…
We study regularity properties for solutions to elliptic equations that are degenerate or singular along orthogonal hyperplanes. The degenerate ellipticity is carried out by a weight term which is the monomial product of different powers of…
We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…