Related papers: Reconstruction of solutions to a generalized Moisi…
We consider the behavior of generalized Laplacian vector fields on a Jordan domain of $\mathbb{R}^{3}$ with fractal boundary. Our approach is based on properties of the Teodorescu transform and suitable extension of the vector fields.…
There are considered vector fields and quaternionic $\alpha$-hyperholomorphic functions in a domain of $R^2$ which generalize the notion of solenoidal and irrotational vector fields. There are established sufficient conditions for the…
The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is…
In this paper we study the solvability of the magnetohydrostatic equations with Grad-Rubin boundary conditions in general domains. Earlier results for this problem were obtained in the recent years by D. Alonso-Or\'an and J. L. L.…
We study a weak formulation of Serrin's overdetermined boundary value problem in planar Jordan domains with rectifiable boundary. Our first result establishes that, within the class of rectifiable Jordan Smirnov domains, the corresponding…
We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to prove a uniformization result for compact metric surfaces by…
In this paper, based on a proposed notion of generalized conjugate harmonic pairs in the framework of complex Clifford analysis, necessary and sufficient conditions for the solvability of inhomogeneous perturbed generalized…
We consider the planar unit disk $\mathbb D$ as the reference configuration and a Jordan domain $\mathbb Y$ as the deformed configuration, and study the problem of extending a given boundary homeomorphism $\varphi \colon \partial \mathbb D…
It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for the…
We show that arbitrary homeomorphic solutions to the Beltrami equations with generalized derivatives satisfy certain moduli inequalities. On this basis, we develope the theory of the boundary behavior of such solutions and prove a series of…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
In this paper, general quaternionic structure are developed for the local fractional Moisil-Teodorescu operator in Cantor-type cylindrical and spherical coordinate systems. Two examples for the Helmholtz equation with local fractional…
This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen,…
With no criteria of the index type, it is proved the existence of a solution for the Riemann-Hilbert problem in the fairly general setting of arbitrary Jordan domains, measurable coefficients and measurable boundary data. The theorem is…
We are interested in the numerical reconstruction of a vector field with prescribed divergence and curl in a general domain of R 3 or R 2 , not necessarily contractible. To this aim, we introduce some basic concepts of finite element…
In \cite{CJ1} M. Jaoua et al. studied the linear approximation of Robin problem on $\Omega$ an open bounded domain of $\R^d$, and they given some important results. In this paper, we study a nonlinear approximation of an elliptic problem…
This paper is concerned with the global well-posedness of a chemotaxis-Euler system in bounded domains of $\mathbb{R}^2$. Completing the system with physical boundary conditions, we show that the corresponding initial boundary value problem…
The initial boundary value problems for compressible Navier-Stokes-Poisson is considered on a bounded domain in $\mathbb{R}^3$ in this paper. The global existence of smooth solutions near a given steady state for compressible…
By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained,…
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…