相关论文: $L^\infty$-variational problems associated to meas…

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…

All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates.…

In this article we study convexity properties of distance functions in infinite dimensional Finsler unitary groups, such as the full unitary group, the unitary Schatten perturbations of the identity and unitary groups of finite von Neumann…

It is proved that vertical graphs and radial graphs are strongly stable for a certain type of densities in Euclidean space ${\mathbb R}^{n+1}$. Particular cases of these densities include translators, expanders and singular minimal…

We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we…

Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the…

The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and…

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…

We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain…

Here, the concept of electric capacity on Finsler spaces is introduced and the fundamental conformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact Finsler manifold is conformal invariant. This…

We consider in this work the problem of minimizing the von Neumann entropy under the constraints that the density of particles, the current, and the kinetic energy of the system is fixed at each point of space. The unique minimizer is a…

We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive…

Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…

In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.

In this paper we discuss the Mather problem for stationary Lagrangians, that is Lagrangians $L:\Rr^n\times \Rr^n\times \Omega\to \Rr$, where $\Omega$ is a compact metric space on which $\Rr^n$ acts through an action which leaves $L$…

We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$.…

A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial…

We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental…

This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the langrangian surfaces of a Kaehler surface, or, more generally, a symplectic 4-manifold with suitable…

We formulate a variational principle for a collection of projectors in an indefinite inner product space. The existence of minimizers is proved in various situations.