相关论文: Green's formulas for cone differential operators
The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of…
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…
We derive a variational formula for the outward normal derivative of the Green function for the Schr\"odinger and Laplace--Beltrami operators, viewed as perturbations of the Laplacian. As an application we begin to characterize elliptic…
We show the completeness of the system of generalized eigenfunctions of closed extensions of elliptic cone operators under suitable conditions on the symbols.
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We prove subelliptic estimates for ethe complex Green operator $ K_q $ at a specific level $ q $ of the $ \bar\partial_b $-complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition.…
We describe various ways of obtaining the Hadamard coefficients associated to a normally hyperbolic operator from the corresponding Green's operators. As the Hadamard expansion on its own is not enough for this, we include additional…
Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. It has previously been shown that if the random environment is translational invariant, then the averaged…
This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of the trace $\Tr Pe^{-tA}$, where $A$ is an elliptic cone differential operator for which the resolvent exists on a suitable region of the…
We define the concept of completely regular ordinary differential operators and give various criteria for operators to belong to this class. We give also criteria for Birkhof regularity of ordinary differential operators in terms of the…
It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of…
We compute fundamental solutions of homogeneous elliptic differential operators, with constant coefficients, on $\mathbb{R}^n$ by mean of analytic continuation of distributions. The result obtained is valid in any dimension, for any degree…
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses and on the regularity of the solutions to the associated…
We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series…
Using the generalisation of Zhu's recursion relations to N=2 superconformal field theories we construct modular covariant differential operators for weak Jacobi forms. We show that differential operators of this type characterise the…