Related papers: Vector variational principle

A variation on the splitting principle

In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…

We prove a variation of Gronwall's lemma.

An equivalent but useful version on the Homological Nerve Theorem is proved.

We prove a conditional expectation bang-bang principle. Based on properties of the conditional expectation vector measure, we establish that the conditional expectation of a set-valued mapping coincides with the conditional expectation of…

A proof of Sendov's conjecture is given.

An technically interesting proof of a known theorem.

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…

A generalization of the law of total covariance is presented and proved.

Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

We provide a simple proof of a result, due to G. Alberti, concerning a rank-one property for the singular part of the derivative of vector-valued functions of bounded variation.

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.

We prove the optimal regularity for some class of vector-valued variational inequalities with gradient constraints. We also give a new proof for the optimal regularity of some scalar variational inequalities with gradient constraints. In…

In this paper, we establish a partial order principle, which is useful to deriving vector Ekeland variational principle (denoted by EVP). By using the partial order principle and extending Gerstewitz's functions, we obtain a vector EVP for…

A proof is given of Rosenthal's \(\ell_1\) theorem.

We prove martingale-ergodic and ergodic-martingale theorems for vector valued Bochner integrable functions. We obtain dominant and maximal inequalities. We also prove weighted and multiparameter martingale-ergodic and ergodic martingale…

Assume that A is a bounded selfadjoint operator in a Hilbert space H. Then, the variational principle is obtained for some functional. As an application of this principle, a variational principle for the electrical capacitance of a…

Based on the principle of causality, I advance a new principle of variation and try to use it as the most general principle for research into laws of nature.

By analyzing degeneracy loci over projectivized vector bundles, we recompute the degree of the discriminant locus of a vector bundle and provide a new proof of the Bogomolov instability theorem.