相关论文: Floquet Problem and Center Manifold Reduction for …

We study cocycles (non-autonomous dynamical systems) satisfying a certain squeezing condition with respect to the quadratic form of a bounded self-adjoint operator acting in a Hilbert space. We prove that (under additional assumptions) the…

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new…

The homogenization of elliptic divergence-type fourth-order operators with periodic coefficients is studied in a (periodic) domain. The aim is to find an operator with constant coefficients and represent the equation through a perturbation…

This work is about global H\"older regularity for solutions to elliptic partial differential equations subject to mixed boundary conditions on irregular domains. There are two main results. In the first, we show that if the domain of the…

We study resolvent approximations for elliptic differential nonselfadjoint operators with periodic coefficients in the limit of the small period. The class of operators covered by our analysis includes uniformly elliptic families with…

We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the…

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…

In this paper, we consider periodic boundary value problems for differential equations whose coefficients are trigonometric polynomials. We construct the spaces of generalized functions, where such problems have solutions. In particular,…

The aim of our paper is to formulate and solve problems concerning linear multiple periodic recurrence equations. Among other things, we discuss in detail the cases with periodic and multi-periodic coefficients, highlighting in particular…

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…

We compute fundamental solutions of homogeneous elliptic differential operators, with constant coefficients, on $\mathbb{R}^n$ by mean of analytic continuation of distributions. The result obtained is valid in any dimension, for any degree…

We study the Dirichlet problem in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order, with bounded, complex-valued coefficients. Our main result gives a sharp condition…

In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative…

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…

In this paper we show how a second order scalar uniformly elliptic equation on divergence form with measurable coefficients and Dirichlet boundary conditions can be transformed into a first order elliptic system with half-Dirichlet boundary…

We study uniform Lipschitz regularity estimates for elliptic systems in divergence form with continuous coefficients, based on rapidly oscillating periodic coefficients derived from homogenization theory. We extend a result by Avellaneda…

We develop a spectral low-mode reduced solver for second-order elliptic boundary value problems with spatially varying diffusion coefficients. The approach projects standard finite difference or finite element discretization onto a global…

Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…

We study the Dirichlet problem for a second-order elliptic operator $L^*$ in double divergence form, also known as the stationary Fokker-Planck-Kolmogorov equation. Assuming that the leading coefficients have Dini mean oscillation, we…