Related papers: Fundamental solutions of homogeneous elliptic diff…
We prove $L_p$ estimates of solutions to a conormal derivative problem for divergence form complex-valued higher-order elliptic systems on a half space and on a Reifenberg flat domain. The leading coefficients are assumed to be merely…
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…
This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on…
The classical Hormander's inequality for linear partial differential operators with constant coeffcients is extended to pseudodifferential operators.
It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a…
Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev…
Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales for heat transfer and elasticity. When microstructural features of a material have rapid, periodic fluctuations, the solution…
A continuous solution of an algebraic equation with holomorphic almost periodic coefficients is also almost periodic.
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock…
In this work we study the homogenization problem for (nonlinear) eigenvalues of quasilinear elliptic operators. We prove convergence of the first and second eigenvalues and, in the case where the operator is independent of $\varepsilon$,…
For a general ordinary differential operator $\mathcal{L}$ with periodic coefficients we prove that the characteristic polynomial of the Floquet matrix is irreducible over the field of meromorphic functions. We also consider a multipoint…
We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable…
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar…
One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost…
We show that an elliptic uniform pseudodifferential operator over a manifold of bounded geometry defines a class in uniform K-homology, and that this class only depends on the principal symbol of the operator.
In this manuscript, we deal with some particular type of homogeneous first order linear systems with variable coefficients, in which we provide qualitative properties of the solution. When the coefficients of the indeterminate functions are…
We prove the homogenization of the Dirichlet problem for fully nonlinear elliptic operators with periodic oscillation in the operator and of the boundary condition for a general class of smooth bounded domains. This extends the previous…