Related papers: A Second-Order Nonlocal Approximation for Manifold…

One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…

We study a fundamental class of regression models called the second order linear model (SLM). The SLM extends the linear model to high order functional space and has attracted considerable research interest recently. Yet how to efficiently…

In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of…

We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time series models. We show the proposed estimators are consistent and follow normal distributions in…

We study the Poisson equation in a perforated domain with homogeneous Dirichlet boundary conditions. The size of the perforations is denoted by $\epsilon$ > 0, and is proportional to the distance between neighbouring perforations. In the…

On a bounded domain $\Omega\subset\mathbb R^{n+1}$, $n\geq2$, satisfying the corkscrew condition and with Ahlfors regular boundary, we characterize the dual space to the space ${\bf N}_{2,p}$ of functions $u$ whose Kenig-Pipher modified…

We prove local convergence of the $t$-PNG model with zero boundary to the stationary $t$-PNG model, confirming a recent conjecture of Drillick and Lin (2024). The stationary $t$-PNG model is the one with both left and bottom boundaries of…

We consider the solution of second order elliptic PDEs in $\R^d$ with inhomogeneous Dirichlet data by means of an $h$-adaptive FEM with fixed polynomial order $p\in\N$. As model example serves the Poisson equation with mixed…

In this work, we analyze a penalized variant of the {\phi}-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The {\phi}-FEM is a recently introduced unfitted finite element method based on a level-set description of…

Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal…

In this work, we study the Dirichlet problem associated with a strongly coupled system of nonlocal equations. The system of equations comes from a linearization of a model of peridynamics, a nonlocal model of elasticity. It is a nonlocal…

We prove results on solvability of nonlinear elliptic partial differential systems of principle type of second order. They are consequences of existence of non-radial solutions for nonlinear partial differential systems of Poisson type. As…

Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We…

We investigate the dependence of optimal constants in Poincar\'e- Sobolev inequalities of planar domains on the region where the Dirichlet condition is imposed. More precisely, we look for the best Dirichlet regions, among closed and…

The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and…

Using standard intrusive techniques when solving hyperbolic conservation laws with uncertainties can lead to oscillatory solutions as well as nonhyperbolic moment systems. The Intrusive Polynomial Moment (IPM) method ensures hyperbolicity…

Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…

In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of…

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with…

In this paper we deal with the well-posedness of Dirichlet problems associated to nonlocal Hamilton-Jacobi parabolic equations in a bounded, smooth domain $\Omega$, in the case when the classical boundary condition may be lost. We address…