Related papers: Variational principles for self-adjoint operator f…
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…
For proper lower semi-continuous functionals bounded below which do not increase upon polarization, an improved version of Ekeland's variational principle can be formulated in Banach spaces, which provides almost symmetric points.
In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be…
For classical dynamical systems time operators are introduced as selfadjoint operators satisfying the so called weak Weyl relation with the unitary groups of time evolution. Dynamical systems with time operators are intrinsically…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
Let $1 \leq m \leq n$ be two integers and $\Omega \Subset \C^n$ a bounded $m$-hyperconvex domain in $\C^n$. Using a variational approach, we prove the existence of the first eigenvalue and an associated eigenfunction which is…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form \[ \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) \] and prove perturbation results and…
We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for…
We propose, as an alternative theory of quantum mechanics, a relativistically covariant variational principle (VP) capable of describing both wavefunction collapse and, as an appropriate limiting case, evolution of the wavefunction…
We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with…
The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Holderian functions. In particular, it…
We prove an entanglement principle for fractional Laplace operators on $\mathbb R^n$ for $n\geq 2$ as follows; if different fractional powers of the Laplace operator acting on several distinct functions on $\mathbb R^n$, which vanish on…
With the dual variational principle and the saddle point reduction we use the abstract bifurcation theory recently developed by author in previous work to prove many new bifurcation results for solutions of four types of Hamiltonian…
We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal…
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…