相关论文: On the Green's matrices of strongly parabolic syst…

We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…

We establish global Gaussian estimates for the Green's matrix of divergence form, second order parabolic systems in a cylindrical domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a…

We study Green's matrices for divergence form, second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains. We establish existence, uniqueness, and pointwise estimates of the Green's matrices.

We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…

In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable coefficients in $\mathbb{R}^n$ and for the corresponding…

We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local…

In this paper, we are concerned with divergence form, higher-order parabolic systems in a cylindrical domain with a finite number of subdomains. We establish $L_\infty$ and Schauder estimates of solutions when the leading coefficients and…

We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…

We study the Neumann Green's function for second order parabolic systems in divergence form with time-dependent measurable coefficients in a cylindrical domain $\mathcal{Q}=\Omega\times (-\infty,\infty)$, where $\Omega\subset \mathbb{R}^n$…

We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that…

We prove Schauder estimates for solutions to both divergence and non-divergence type higher-order parabolic systems in the whole space and the half space. We also provide an existence result for divergence type systems in a cylindrical…

We consider divergence form, second-order strongly parabolic systems in a cylindrical domain with a finite number of subdomains under the assumption that the interfacial boundaries are $C^{1,\text{Dini}}$ and $C^{\gamma_{0}}$ in the spatial…

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable…

In this paper we develop a theory of linear differential systems analogous to the classical one for ODEs, including the obtaining of fundamental matrices, the development of a variation of parameters formula and the expression of the…

We establish several gradient estimates for second-order divergence type parabolic and elliptic systems. The coefficients and data are assumed to be H\"older or Dini continuous in the time variable and all but one spatial variables. This…

We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…

A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

We consider time-inhomogeneous, second order linear parabolic partial differential equations of the non-divergence type, and assume the ellipticity and the continuity on the coefficient of the second order derivatives and the boundedness on…