Related papers: Variational problems without having any non-trivia…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
We consider generalized (possibly depending on fields as well as on space-time variables) gauge transformations and gauge symmetries in the context of general -- that is, possibly non variational nor covariant -- differential equations. In…
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary value…
The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…
This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-invariant metric, and for its corresponding Riemannian…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a…
For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an $\hbox{Ad}$-invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem…
We develop the new variational calculus introduced in 2011 by J. Cresson and I. Greff, where the classical derivative is substituted by a new complex operator called the scale derivative. In this paper we consider several nondifferentiable…
We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and…
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…
We prove an equivariant implicit function theorem for variational problems that are invariant under a varying symmetry group (corresponding to a bundle of Lie groups). Motivated by applications to families of geometric variational problems…
Gauge symmetries lead to first-class constraints. This assertion is of course true only for non trivial gauge symmetries, i.e., gauge symmetries that act non trivially on-shell on the dynamical variables. We illustrate this well-appreciated…
After the introduction of $\lambda$-symmetries by Muriel and Romero, several other types of so called "twisted symmetries" have been considered in the literature (their name refers to the fact they are defined through a deformation of the…
K. Grove, L. Verdiani, B. Wilking and W. Ziller gave the first examples of cohomogeneity one manifolds which do not carry invariant metrics with non-negative sectional curvatures. In this paper we generalize their results to a larger…
The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…
A pair of linearly independent asymptotic solutions are constructed for the second-order linear difference equation {equation*} P_{n+1}(x)-(A_{n}x+B_{n})P_{n}(x)+P_{n-1}(x)=0, {equation*} where $A_n$ and $B_n$ have asymptotic expansions of…