关于分数阶 Sobolev 空间中 Fredholm 边值问题的可解性

关于在 $C^{n} $ 空间中普通微分系统线性边值问题可解性的研究

Solvability of linear boundary-value problems for ordinary differential systems in the space $C^{n}$

本文研究了在$C^n$空间中普通微分系统线性边值问题的可解性，探讨了边界条件对问题算子的影响，并证明了相关算子的Fredholm性质及极限定理。

Sobolev空间中具有一般非齐次边界条件的微分系统

On Differential Systems in Sobolev spaces with Generic Inhomogeneous Boundary Conditions

本文在Sobolev空间中研究了具一般非齐次边界条件的任意阶常微分方程线性系统，证明了边值问题的Fredholm性质并求出核与余核维数，同时给出解关于参数连续的充要条件。

Solvability of inclusions of Hammerstein type

A fairly general continuation theorem of Leray-Schauder type for the class of so-called admissible multimaps is set forth. This result is then used to establish a universal rule for solving operator inclusions of Hammerstein type in Lebesgue-Bochner spaces. Examples illustrating the legitimacy of this approach include the initial value problem for perturbation of $m$-accretive mutivalued differential equations, the anti-periodic problem for semilinear differential inclusions, abstract integral inclusions of Fredholm and Volterra type and the two-point boundary value problem for nonlinear evolu…

On Linear Boundary-Value Problems for Differential Systems in Sobolev spaces

We consider the Fredholm one-dimensional boundary-value problems in Sobolev spaces.We have obtained several important results about the indixes of functional operators, the criterion of their correct well-posedness, the criterion of the continuous dependence of the solutions of these problems on the parameter, the degree of convergence of these solutions, and sufficient constructive conditions under which the solutions of the most general class of multipoint boundary-value problems are continuous with respect to the parameter. Eeach of these boundary-value problems corresponds to a certain rec…

粗糙区域中正则性问题与 Poisson 正则性问题可解性的外推

Extrapolation of solvability of the regularity and the Poisson regularity problems in rough domains

本文研究无连通性假设的 Ahlfors 正则粗糙边界区域，建立椭圆正则性问题在 Hajłasz-Sobolev 空间 $M^{1,1}$ 中的可解性向 $M^{1,p}$ 的外推，并推广至帐篷空间上的 Poisson 正则性问题及 Hardy-Sobolev 可解性。

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second order, complex, elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning \textit{a priori} almost everywhere no…

Sobolev空间中具有一般非齐次边界条件的微分系统

Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions

本文综述了Sobolev空间中带一般非齐次边界条件的任意阶线性常微分方程组，建立了Fredholm性质并给出指标及核与余核维数，同时得到解关于参数连续性的充要条件。

The factorization technique for difference equations

We study multidimensional difference equations with a continual variable in the Sobolev--Slobodetskii spaces. Using ideas and methods of the theory of boundary value problems for elliptic pseudo differential equations we suggest to consider certain boundary value problems for such difference equations. Special boundary conditions permit to prove unique solvability for these boundary value problems in appropriate Sobolev--Slobodetskii spaces.