Related papers: On the Reifenberg Plateau Problem in Hilbert space

In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family…

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study…

We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional…

This paper is a survey paper on old and recent results on direction problems in finite dimensional affine spaces over a finite field.

In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen…

We solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicity.

We establish existence and multiplicity of solutions for a elliptic resonant elliptic problem under Dirichlet boundary conditions.

In the paper, we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in $L^2_{x,v}\cap L^\infty_{x,v}$ in half-space. The uniqueness, continuity and exponential decay of the…

In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…

In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.

This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…

We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…

In this paper the Navier problem and the Dirichlet problem for Willmore curves in $\mathbb{R}^2$ is solved.

A Hilbert space frame on $R^n$ is {\it scalable} if we can scale the vectors to make them a tight frame. There are known classifications of scalable frames. There are two basic questions here which have never been answered in any $R^n$:…

We focused on the Ablowitz--Ladik equation on a zero background, specifically considering the scenario of $N$ pairs of multiple poles. Our first goal was to establish a mapping between the initial data and the scattering data. This allowed…

This paper aims to propose a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of $d$-rectifiable closed subsets of $\mathbb…

We investigate thin-slit diffraction problems for two-dimensional lattice waves. The peculiar structure allows us to consider the problems on the semi-infinite triangular lattice, consequently, we study Dirichlet problems for the…

We propose a new approach to studying classical solutions of the Bellman equation and Master equation for mean field type control problems, using a novel form of the "lifting" idea introduced by P.-L. Lions. Rather than studying the usual…

An inverse problem of elasticity of $n$ elastic inclusions embedded into an elastic half-plane is analyzed. The boundary of the half-plane is free of traction. The half-plane and the inclusions are subjected to antiplane shear, and the…

The paper is devoted to investigating a Cauchy problem for nonlinear elliptic PDEs in the abstract Hilbert space. The problem is hardly solved by computation since it is severely ill-posed in the sense of Hadamard. We shall use a modified…