Entropy solutions for nonhomogeneous anisotropic $Δ_{p⃗(·)}$ problems

Elhoussine Azroul; Abdelkrim Barbara; Mohamed Badr Benboubker; Hassane Hjiaj

Displaying similar documents to “Entropy solutions for nonhomogeneous anisotropic $Δ_{p ⃗ (\cdot)}$ problems”

Operator entropy inequalities

M. S. Moslehian, F. Mirzapour, A. Morassaei (2013)

Colloquium Mathematicae

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We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting $S_{q}^{f} (A | B) : = \sum_{j = 1}^{n} A_{j}^{1 / 2} {(A_{j}^{- 1 / 2} B_{j} A_{j}^{- 1 / 2})}^{q} f (A_{j}^{- 1 / 2} B_{j} A_{j}^{- 1 / 2}) A_{j}^{1 / 2}$ , and then give upper and lower bounds for $S_{q}^{f} (A | B)$ as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004),...

A local approach to $g$ -entropy

Mehdi Rahimi (2015)

Kybernetika

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In this paper, a local approach to the concept of $g$ -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of $g$ -entropy.

On Pawlak's problem concerning entropy of almost continuous functions

Tomasz Natkaniec, Piotr Szuca (2010)

Colloquium Mathematicae

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We prove that if f: → is Darboux and has a point of prime period different from $2^{i}$ , i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.

Continuous dependence of the entropy solution of general parabolic equation

Mohamed Maliki (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider the general parabolic equation : $u_{t} - Δ b (u) + d i v F (u) = f$ in $Q =] 0, T [\times ℝ^{N}, T > 0$ with $u_{0} \in L^{\infty} (ℝ^{N}),$ $for a . e t \in] 0, T [, f (t) \in L^{\infty} (ℝ^{N})$ and $\int_{0}^{T} {∥f (t)∥}_{L^{\infty} (ℝ^{N})} d t < \infty .$ We prove the continuous dependence of the entropy solution with respect to $F,$ $b,$ $f$ and the initial data $u_{0}$ of the associated Cauchy problem. This type of solution was introduced and studied in [MT3]. We start by recalling the definition of weak solution and entropy solution. By applying an abstract result (Theorem...

Further results on the generalized cumulative entropy

Antonio Di Crescenzo, Abdolsaeed Toomaj (2017)

Kybernetika

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Recently, a new concept of entropy called generalized cumulative entropy of order $n$ was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results...

Orders of accumulation of entropy

David Burguet, Kevin McGoff (2012)

Fundamenta Mathematicae

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For a continuous map T of a compact metrizable space X with finite topological entropy, the order of accumulation of entropy of T is a countable ordinal that arises in the context of entropy structures and symbolic extensions. We show that every countable ordinal is realized as the order of accumulation of some dynamical system. Our proof relies on functional analysis of metrizable Choquet simplices and a realization theorem of Downarowicz and Serafin. Further, if M is a metrizable Choquet...

Sequence entropy and rigid σ-algebras

Alvaro Coronel, Alejandro Maass, Song Shao (2009)

Studia Mathematica

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We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,,ν,T) be a factor of a measure-theoretical dynamical system (X,,μ,T) and S be a sequence of positive integers with positive upper density. We prove there exists a subsequence A ⊆ S such that $h_{μ}^{A} (T, ξ |) = H_{μ} (ξ | (X | Y))$ for all finite partitions ξ, where (X|Y) is the Kronecker algebra over . A similar result holds for rigid algebras over . As an application, we characterize compact, rigid and mixing extensions via relative...

A representation theorem for perfect partitions of $Z^{2}$ -actions with finite entropy

B. Kamiński (1988)

Colloquium Mathematicae

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Margulis Lemma, entropy and free products

Filippo Cerocchi (2014)

Annales de l’institut Fourier

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We prove a Margulis’ Lemma Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product $A * B$ , without 2-torsion. Moreover, if $A * B$ is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds. ...

The topological entropy versus level sets for interval maps (part II)

Jozef Bobok (2005)

Studia Mathematica

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Let f: [a,b] → [a,b] be a continuous function of the compact real interval such that (i) $c a r d f^{- 1} (y) \geq 2$ for every y ∈ [a,b]; (ii) for some m ∈ ∞,2,3,... there is a countable set L ⊂ [a,b] such that $c a r d f^{- 1} (y) \geq m$ for every y ∈ [a,b]∖L. We show that the topological entropy of f is greater than or equal to log m. This generalizes our previous result for m = 2.

Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and $L^{1}$ -data

Abdelali Sabri, Ahmed Jamea, Hamad Talibi Alaoui (2020)

Communications in Mathematics

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In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic $p (\cdot)$ -Laplacian problem with Dirichlet-type boundary conditions and $L^{1}$ data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.

Spaces of Lipschitz type, embeddings and entropy numbers

Edmunds D. E., Haroske D.

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AbstractWe establish the sharpness of the embedding of certain Besov and Triebel-Lizorkin spaces in spaces of Lipschitz type. In particular, this proves the sharpness of the Brézis-Wainger result concerning the “almost” Lipschitz continuity of elements of the Sobolev space $H_{p}^{1 + n / p} (ℝ ⁿ)$ , where 1 < p < ∞. Upper and lower estimates are obtained for the entropy numbers of related embeddings of Besov spaces on bounded domains. CONTENTSIntroduction...........................................................51....

Jumps of entropy for $C^{r}$ interval maps

David Burguet (2015)

Fundamenta Mathematicae

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We study the jumps of topological entropy for $C^{r}$ interval or circle maps. We prove in particular that the topological entropy is continuous at any $f \in C^{r} ([0, 1])$ with $h_{t o p} (f) > (l o g ⁺ | | f^{'} {| |}_{\infty}) / r$ . To this end we study the continuity of the entropy of the Buzzi-Hofbauer diagrams associated to $C^{r}$ interval maps.

Symbolic extensions for nonuniformly entropy expanding maps

David Burguet (2010)

Colloquium Mathematicae

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A nonuniformly entropy expanding map is any ¹ map defined on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a $^{r}$ nonuniformly entropy expanding map T with r > 1 has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T. Downarowicz and A. Maass [Invent. Math. 176 (2009)].

A strongly degenerate quasilinear equation : the elliptic case

Fuensanta Andreu, Vicent Caselles, José Mazón (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation $u - div 𝐚 (u, D u) = v$ , where $v \in L^{1}$ , $𝐚 (z, ξ) = \nabla_{ξ} f (z, ξ)$ , and $f$ is a convex function of $ξ$ with linear growth as $∥ ξ ∥ \to \infty$ , satisfying other additional assumptions. In particular, this class includes the case where $f (z, ξ) = ϕ (z) ψ (ξ)$ , $ϕ > 0$ , $ψ$ being a convex function with linear growth as $∥ ξ ∥ \to \infty$ . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions...

Displaying similar documents to “Entropy solutions for nonhomogeneous anisotropic Δ p ⃗ ( · ) problems”

Displaying similar documents to “Entropy solutions for nonhomogeneous anisotropic $Δ_{p ⃗ (\cdot)}$ problems”