相关论文: Higher order analogues of exterior derivative

The existence of higher derivative discontinuous solutions to a first order ordinary differential equation is shown to reveal a nonlinear SL(2,R) structure of analysis in the sense that a real variable $t$ can now accomplish changes not…

We suggested an algorithm for searching the recursion operators for nonlinear integrable equations. It was observed that the recursion operator $R$ can be represented as a ratio of the form $R=L_1^{-1}L_2$ where the linear differential…

We estimate the second order linking invariants of Lipschitz maps from an n-dimensional ellipse. The estimate uses a new directionally-dependent version of the isoperimetric inequality for cycles inside the ellipse. Using this work, we…

In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…

We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…

The main aim of this article is to establish an $L_p$-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the…

We obtain regularity conditions of a new type of problems of the calculus of variations with second-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main result asserts that autonomous integral…

New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…

We consider self-adjoint extensions of differential operators of the type $ (-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and…

Interpolation inequalities for $C^m$ functions allow to bound derivatives of intermediate order $0 < j<m$ by bounds for the derivatives of order $0$ and $m$. We review various interpolation inequalities for $L^p$-norms ($1 \le p \le…

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of…

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…

The linear differential operator with constant coefficients $$D(y)=y^{(n)}+a_1 y^{(n-1)}+\ldots+a_n y,\quad y\in \mathcal{C}^{n}(\mathbb{R}, X)$$ acting in a Banach space $X$ is Ulam stable if and only if its characteristic equation has no…

Let $k$ be a differential field of characteristic zero and $E$ be a liouvillian extension of $k$. For any differential subfield $K$ intermediate to $E$ and $k$, we prove that there is an element in the set $K-k$ satisfying a linear…

In this paper, we establish various L2-estimates for the exterior differential operator on p-convex Riemannian manifolds in the sense of Harvey and Lawson. As geometric applications, we prove vanishing and finiteness results for the de Rham…

For any non-negative integer v we construct explicitly [v/2]+1 independent covariant bilinear differential operators from J_{k,m} x J_{k',m'} to J_{k+k'+v,m+m'}. As an application we construct a covariant bilinear differential operator…

We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also…

We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes of vertex operators. A linear operator…