Related papers: Convex integration with linear constraints and its…
Singular fourth-order Abreu equations have been used to approximate minimizers of convex functionals subject to a convexity constraint in dimensions higher than or equal to two. For Abreu type equations, they often exhibit different…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
We study sets defined as the intersection of a rank-1 constraint with different choices of linear side constraints. We identify different conditions on the linear side constraints, under which the convex hull of the rank-1 set is polyhedral…
Let $k$ be a differential field of characteristic zero and $E$ be a liouvillian extension of $k$. For any differential subfield $K$ intermediate to $E$ and $k$, we prove that there is an element in the set $K-k$ satisfying a linear…
We study radial symmetry of large solutions of the semi-linear elliptic problem \Delta u + \nabla h.\nabla u = f(|x|,u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of…
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we…
Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…
In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted…
In this short paper, a matrix perturbation bound on the eigenvalues found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
In this paper, we show the existence and multiplicity of solutions for the following fourth-order Kirchhoff type elliptic equations \begin{eqnarray*} \Delta^{2}u-M(\|\nabla u\|_{2}^{2})\Delta u+V(x)u=f(x,u),\ \ \ \ \ x\in \mathbb{R}^{N},…
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
We give a self-contained introduction to the relations between Integrable Systems and the Geometry of Riemann Surfaces. We start from a historical introduction to the topic of integrable systems. Afterwards, we study the polynomial…
We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
A theorem on the solutions of the problem $U'(w)=\gamma F(U(w),w),\ U(w_1)=u_2,\ U(w_2)=u_2$ is applied for finding the functional solutions of the system of partial differential equations \begin{equation} \nabla\cdot(a(u,w)\nabla u)=0,\…
A unified construction of $H(\textrm{div})$-conforming finite element tensors, including vector element, symmetric matrix element, traceless matrix element, and, in general, tensors with linear constraints, is developed in this work. It is…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
We consider the following convective Neumann systems:\begin{equation*}\left(\mathrm{S}\right)\qquad\left\{\begin{array}{ll}-\Delta_{p_1}u_1+\frac{|\nabla u_1|^{p_1}}{u_1+\delta_1}=f_1(x,u_1,u_2,\nabla u_1,\nabla u_2) & \text{in}\;\Omega,\\…