Related papers: Nonsmooth Pseudodifferential Boundary Value Proble…
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…
If M is a compact oriented manifold-with-boundary whose fundamental group is virtually nilpotent or Gromov-hyperbolic, we show that the higher signatures of M are oriented-homotopy invariants.
The linear PDE ${\mathbf B} {\mathbf L} (\frac{\partial}{\partial x}) u ={\mathbf L}_1(\frac{\partial}{\partial x})u +f(x)$ with nonclassic conditions on boundary $\partial \Omega$ is considered. Here ${\mathbf B}$ is linear noninvertible…
In this paper we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements…
This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives with nonlocal boundary conditions. We investigate the Green function and some of its…
In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators on manifolds with boundary. We also consider applications to curvature prescription problems on manifolds…
We reformulate all general real coupled self-adjoint boundary value problems as integral operators and show that they are all finite rank perturbations of the free space Green's function on the real line. This free space Green's function…
We prove sufficient conditions in order to obtain a sharp G\aa rding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp G\aa rding inequality for compact…
In this paper, we consider the Dirichlet boundary value problem for fully nonlinear Yamabe equations on Riemannian manifolds with boundary. Assuming the existence of a subsolution, we derive \emph{a priori} boundary second derivative…
Qualitative and quantitative aspects for variational inequalities governed by strongly pseudomonotone operators on Hilbert space are investigated in this paper. First, we establish a global error bound for the solution set of the given…
In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…
We study the low energy resolvent of the Hodge Laplacian on a manifold equipped with a fibred boundary metric. We determine the precise asymptotic behavior of the resolvent as a fibred boundary (aka $\phi$-) pseudodifferential operator when…
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively…
We study pseudo-differential operators on a wedge with continuous and variable discrete branching asymptotics.
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
We present in this paper the construction of a pseudodifferential calculus on smooth non-compact manifolds associated to a globally defined and coordinate independant complete symbol calculus, that generalizes the standard…
In this paper the boundary value problem for one class of the operator-differential equations of the third order on a semi-axis, where one of the boundary conditions is perturbed by some linear operator is researched. There are received…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We consider the discrete, fractional operator $\left(L_a^\nu x\right) (t) := \nabla [p(t) \nabla_{a^*}^\nu x(t)] + q(t) x(t-1)$ involving the nabla Caputo fractional difference, which can be thought of as an analogue to the self-adjoint…