Related papers: A duality theory for some non-convex functions of …
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
For the Lie algebra $\g$ of a connected infinite-dimensional Lie group~$G$, there is a natural duality between so-called semi-equicontinuous weak-*-closed convex Ad^*(G)-invariant subsets of the dual space $\g'$ and Ad(G)-invariant lower…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
We propose models in nonlinear elasticity for nonsimple materials that include surface energy terms. Additionally, we also discuss living surface loads on the boundary. We establish corresponding linearized models and show their…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…
In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particular, we show that if the nonlinear term possesses a special…
We describe forms with non-Abelian charges. We avoid the use of theories with flat curvatures by working in the context of topological field theory. We obtain TQFTs for a form and its dual. We leave open the question of getting gauges in…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…
It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude…
An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from the interior of the cone. The main facts of the duality…
We review the passage from the supermembrane to matrix theory via a consistent truncation following a non-commutative deformation in light-cone gauge. Some indications are given that there should exist a generalisation of non-commutativity…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
A new T-duality transformation is found in two-dimensional non-linear sigma models. This is a straightforward generalisation of Abelian and non-Abelian T-dualities.
Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form.…