Related papers: Covariant Poisson equation with compact Lie algebr…
The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…
Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show…
In this paper, we consider the versal deformations of three dimensional Lie algebras. We classify Lie algebras and study their deformations by using linear algebra techniques to study the cohomology. We will focus on how the deformations…
The Riemann Mapping Theorem states existence of a conformal homeomorphism $\varphi$ of a simply connected plane domain $\Omega\subset\mathbb C$ with non-empty boundary onto the unit disc $\mathbb D\subset \mathbb C$. In the first part of…
For systems of linear differential equations on a compact interval, we investigate the~dependence on a parameter $\varepsilon$ of the solutions to boundary-value problems in the Sobolev spaces $W^{n}_{\infty}$. We obtain a constructive…
A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a…
Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We collect some general results on the Poisson center of S(g), including some simple criteria regarding its polynomiality, and also on…
In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions…
We investigate some multiplication properties of Kato-Sobolev spaces by adapting the techniques used in the study of Beurling algebras by Coifman and Meyer. Also we develop an analytic functional calculus for Kato-Sobolev algebras based on…
The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically…
We study unital commutative associative algebras and their associated n-Lie algebras, showing that they are strong transposed Poisson n-Lie algebras under specific compatibility conditions. Furthermore, we generalize the simplicity…
The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum…
This paper studies the Sobolev regularity of weak solution of degenerate elliptic equations in divergence form $\text{div}[\mathbf{A}(X) \nabla u] = \text{div}[\mathbf{F}(X)]$, where $X = (x,y) \in \mathbb{R}^{n} \times \mathbb{R}$ . The…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are provided by conditions on these tensors, which may be understood as cocycle…
The boundary conditions for canonical vacuum general relativity is investigated at the quasi-local level. It is shown that fixing the area element on the 2- surface S (rather than the induced 2-metric) is enough to have a well defined…
We present a thorough study of the differential geometry of weightings and develop the theory of weightings for vector bundles, Lie groupoids, and Lie algebroids. We begin by extending the work of Loizides and Meinrenken on weighted…
We introduce and study a notion of co-radiantness for set-valued mappings between nonnegative orthants of Euclidean spaces. We analyze them from an abstract convexity perspective. Our main results consist in representations, in terms of…
The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair $(\mathcal{A},\{\cdot_\lambda\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear…
We develop a geometric invariant Littlewood-Paley theory for arbitrary tensors on a compact 2 dimensional manifold. We show that all the important features of the classical LP theory survive with estimates which depend only on very limited…