相关论文: Differential systems in Sobolev spaces with generi…
Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.
First and second-order inequalities of Friedrichs type for Sobolev functions in arbitrary domains are offered. The relevant inequalities involve optimal norms and constants that are independent of the geometry of the domain. Parallel…
A model elliptic pseudo-differential equation in $4$-faced cone is studied in Sobolev--Slobodetskii space. The Bochner kernel for such a cone is evaluated and explicit formula for unique solution to the considered equation is presented…
Semi-linear elliptic boundary problems with non-linearities of product type are considered, in particular the stationary Navier--Stokes equations. Regularity and existence results are dealt with in the Besov and Triebel--Lizorkin spaces,…
We discuss the solvability of an infinite system of first order ordinary differential equations on the half line, subject to nonlocal initial conditions. The main result states that if the nonlinearities possess a suitable "sub-linear"…
Free bondary value problem for elliptic differential-operator equations with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued Holder spaces.
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…
A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the…
We prove existence of a solution to the divergence equation satisfying a new Bogovski-type estimate for the difference quotients. This enables us to give an alternative proof of the interior regularity of the solution to the $p$-Stokes…
We establish a uniform Sobolev inequality for K\"ahler metrics, which only require an entropy bound and no lower bound on the Ricci curvature. We further extend our Sobolev inequality to singular K\"ahler metrics on K\"ahler spaces with…
We lay some mathematically rigorous foundations for the resolution of differential equations with respect to semi-classical bases and topologies, namely Freud-Sobolev polynomials and spaces. In this quest, we uncover an elegant theory…
A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. Boundary-domain integral equations are…
We establish existence, uniqueness, and arbitrary order Sobolev regularity results for the second order parabolic equations with measurable coefficients defined on the conic domains $D$ of the type $$ D(M):=\left\{x\in R^d…
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…
There is studied problem on solvability of linear non-homogeneous differential equation of higher even order. There is proved the theorem on necessary and sufficient conditions on existence of solutions to the equation in the Schwartz…
This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…