A Short Proof of the Variational Principle for a $\mathbb {Z}_{+}^{N}$ Action on a Compact Space

Michal Misiurewicz

Displaying similar documents to “A Short Proof of the Variational Principle for a $ℤ_{+}^{N}$ Action on a Compact Space”

A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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We propose a penalty approach for a box constrained variational inequality problem $(BVIP)$ . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of $BVIP$ when the function $F$ involved is continuous and strongly monotone and the box $C$ contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results...

Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

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We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f : W \to X$ defined on a non-degenerate closed subinterval $W$ of $ℝ^{m}$ in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure $V_{ℳ} F$ generated by the primitive $F : ℐ_{W} \to X$ of $f$ , where $ℐ_{W}$ is the family of all closed non-degenerate subintervals of $W$ .

New extension of the variational McShane integral of vector-valued functions

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

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We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset $G$ of $m$ -dimensional Euclidean space $ℝ^{m}$ . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from $m$ -dimensional closed non-degenerate intervals to open and bounded subsets of $ℝ^{m}$ . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study...

Pressure and recurrence

Véronique Maume-Deschamps, Bernard Schmitt, Mariusz Urbański, Anna Zdunik (2003)

Fundamenta Mathematicae

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We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) $l i m_{n \to \infty} n^{- 1} l o g \sum_{j = 0}^{τ ₙ (x)} μ (α ⁿ (T^{j} (x)))$ , where $α ⁿ (T^{j} (x))$ is the element of the partition containing $T^{j} (x)$ and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).

Finite element variational crimes in the case of semiregular elements

Alexander Ženíšek (1996)

Applications of Mathematics

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The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain $Ω$ whose boundary $\partial Ω$ is formed by two circles $Γ_{1}$ , $Γ_{2}$ with the same center $S_{0}$ and radii $R_{1}$ , $R_{2} = R_{1} + ϱ$ , where $ϱ ≪ R_{1}$ . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for $u = 0$ are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus...