相关论文: Augmented Lagrangian Method for Thin Plates with S…

In bounded domains, without any geometric conditions, we study the existence and uniqueness of globally Lipschitz and interior strong C^{1,1}, (and classical C^2), solutions of general semilinear oblique boundary value problems for…

We study the numerical approximation of time-dependent, possibly degenerate, second-order Hamilton-Jacobi-Bellman equations in bounded domains with nonhomogeneous Dirichlet boundary conditions. It is well known that convergence towards the…

In this paper, we show that the calibrated method can also be used to detect indefinite minimal Lagrangian submanifolds in $C_k^m$. We introduce the notion of indefinite special Lagrangian submanifolds in $C_k^m$ and generalize the…

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend…

We present a Galerkin boundary element method for clamped Kirchhoff--Love plates with piecewise smooth boundary. It is a direct method based on the representation formula and requires the inversion of the single-layer operator and an…

For compact domains with smooth boundaries, we present an approximation scheme for surface spline approximation that delivers precise $L_p$ approximation orders on well known smoothness spaces. This scheme overcomes the boundary effects…

A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us…

In this paper, we study existence and uniqueness of solutions to Jenkins-Serrin type problems on domains in a Riemannian surface. In the case of unbounded domains, the study is focused on the hyperbolic plane.

A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar method is alleviated by…

Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…

Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector. We establish a fully-inhomogeneous version of Gallagher's theorem, a diophantine fibre refinement, and a sharp and unexpected threshold for…

In this paper, we solve the Dirichlet problem with continuous boundary data for the Lagrangian mean curvature equation on a uniformly convex, bounded domain in $\mathbb{R}^n$.

Constrained blackbox optimization is a difficult problem, with most approaches coming from the mathematical programming literature. The statistical literature is sparse, especially in addressing problems with nontrivial constraints. This…

We show that a two-dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we…

We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff-Love plates, including the biharmonic equation as a particular case. The…

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…

We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced…

We analyze the approximation by radial basis functions of a hypersingular integral equation on an open surface. In order to accommodate the homogeneous essential boundary condition along the surface boundary, scaled radial basis functions…

Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic…

We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…