Monotone measures with bad tangential behavior in the plane

Robert Černý; Jan Kolář; Mirko Rokyta

Displaying similar documents to “Monotone measures with bad tangential behavior in the plane”

Concentrated monotone measures with non-unique tangential behavior in $ℝ^{3}$

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Czechoslovak Mathematical Journal

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We show that for every $ε > 0$ there is a set $A \subset ℝ^{3}$ such that $ℋ^{1} ⌞ A$ is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and $ℋ^{1} ⌞ A$ has the $1$ -dimensional density between $1$ and $2 + ε$ everywhere in the support.

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that $λ (V) \leq λ (V_{n})$ where $V_{n}$ is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that $4 / π = λ (l ₂^{(2)}) \geq λ (V)$ for any two-dimensional real symmetric space V.

An alternate proof of Hall's theorem on a conformal mapping inequality.

Balasubramanian, R., Ponnusamy, S. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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Several Differentiation Formulas of Special Functions. Part VI

Bo Li, Pan Wang (2007)

Formalized Mathematics

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In this article, we prove a series of differentiation identities [3] involving the secant and cosecant functions and specific combinations of special functions including trigonometric, exponential and logarithmic functions.

Integrable systems in the plane with center type linear part

Javier Chavarriga (1994)

Applicationes Mathematicae

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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.

Monotonicity of a key function arised in studies of nematic liquid crystal polymers.

Wang, Hongyun, Zhou, Hong (2007)

Abstract and Applied Analysis

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Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

Annales de l'institut Fourier

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We establish a Carleman type inequality for the subelliptic operator $ℒ = Δ_{z} + | x |^{2} \partial_{t}^{2}$ in $ℝ^{n + 1}$ , $n \geq 2$ , where $z \in ℝ^{n}$ , $t \in ℝ$ . As a consequence, we show that $- ℒ + V$ has the strong unique continuation property at points of the degeneracy manifold ${(0, t) \in ℝ^{n + 1} | t \in ℝ}$ if the potential $V$ is locally in certain $L^{p}$ spaces.

Several Differentiation Formulas of Special Functions. Part V

Peng Wang, Bo Li (2007)

Formalized Mathematics

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In this article, we give several differentiation formulas of special and composite functions including trigonometric, polynomial and logarithmic functions.