Related papers: A Note on Flux Integrals over Smooth Regular Domai…
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells,…
We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded…
We theoretically investigate the transfer of angular momentum between a spin superfluid and a domain wall in an exchange coupled easy-axis and easy-plane magnetic insulator system. A domain wall in the easy-axis magnet absorbs spin angular…
The question on expansion of moving volume inside of a smooth flow of the compressible liquid is under consideration. We find a condition on initial data such that if it holds, then within a finite time either the boundary of the moving…
Classically, theorems of Fatou and Julia describe the boundary regularity of functions in one complex variable. The former says that a complex analytic function on the disk has non-tangential boundary values almost everywhere, and the…
We study turbulent flows in pressure-driven ducts with square cross-section through direct numerical simulation in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence.…
1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its entirety. Plain integral manifolds are not enough to…
The paper studies integral functionals with non-smooth functions from L_2 defined on solutions of ODEs. Some regularity is obtained in the form of estimates of L_2-norm for these functionals. This result is used for regularization of…
We discuss without proof some recent advances in the theory of distributional boundary values, and give an example to show that the condition that a piecewise smooth domain has generic corners is necessary for the existence of boundary…
It is well known that a k-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces,…
Consider a random planar point process whose law is invariant under planar isometries. We think of the process as a random distribution of point charges and consider the electric field generated by the charge distribution. In Part I of this…
We consider the vector functions in a domain homeomorphic to a spherical layer bounded by twice continuously differentiable surfaces. Additional restrictions are imposed on the domain, which allow to conduct proofs using simple methods. On…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
As stated in the title, the present research proposes a mathematical definition of laminar and turbulent flows, i.e., a definition that may be used to conceive and prove mathematical theorems about such flows. The definition is based on an…
In this note, we obtain uniqueness results for Beltrami flow in both bounded and unbounded domain with nonempty boundary by establishing an elementary but useful formula involving operators $\divg$ and $\curl$. We also use this formula to…
In this paper the first and second domain variation for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions is computed. Minimality and maximality properties of the ball among nearly circular…