The trace theorem $W^{2,1}_p(\Omega _T) \ni f \mapsto \nabla _{\!x} f \in W^{1-1/p,1/2-1/2p}_p(\partial \Omega _T)$ revisited

Peter Weidemaier

Displaying similar documents to “The trace theorem $W_{p}^{2, 1} (Ω_{T}) ∋ f \mapsto \nabla_{x} f \in W_{p}^{1 - 1 / p, 1 / 2 - 1 / 2 p} (\partial Ω_{T})$ revisited”

Decomposition of the weighted Sobolev space $W^{1, p} (Ω, d_{M}^{ϵ})$ and its traces

Aleš Nekvinda (1993)

Czechoslovak Mathematical Journal

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The fractional dimensional theory in Lüroth expansion

Luming Shen, Kui Fang (2011)

Czechoslovak Mathematical Journal

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It is well known that every $x \in (0, 1]$ can be expanded to an infinite Lüroth series in the form of $x = \frac{1}{d_{1} (x)} + \dots + \frac{1}{d_{1} (x) (d_{1} (x) - 1) \dots d_{n - 1} (x) (d_{n - 1} (x) - 1) d_{n} (x)} + \dots,$ where $d_{n} (x) \geq 2$ for all $n \geq 1$ . In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets $F_{φ} = {x \in (0, 1] : d_{n} (x) \geq φ (n), \forall n \geq 1}$ are completely determined, where $φ$ is an integer-valued function defined on $ℕ$ , and $φ (n) \to \infty$ as $n \to \infty$ .

Entire solutions in $ℝ^{2}$ for a class of Allen-Cahn equations

Francesca Alessio, Piero Montecchiari (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a class of semilinear elliptic equations of the form $- ε^{2} Δ u (x, y) + a (x) W^{'} (u (x, y)) = 0, (x, y) \in ℝ^{2}$ where $ε > 0$ , $a : ℝ \to ℝ$ is a periodic, positive function and $W : ℝ \to ℝ$ is modeled on the classical two well Ginzburg-Landau potential $W (s) = {(s^{2} - 1)}^{2}$ . We look for solutions to (1) which verify the asymptotic conditions $u (x, y) \to \pm 1$ as $x \to \pm \infty$ uniformly with respect to $y \in ℝ$ . We show via variational methods that if $ε$ is sufficiently small and $a$ is not constant, then (1) admits infinitely many of such solutions, distinct up to translations, which do not...

Computing powers of two generalizations of the logarithm.

Zudilin, Wadim (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

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Constructions of smooth and analytic cocycles over irrational circle rotations

Dalibor Volný (1995)

Commentationes Mathematicae Universitatis Carolinae

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We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson,...

Displaying similar documents to “The trace theorem W p 2 , 1 ( Ω T ) ∋ f ↦ ∇ x f ∈ W p 1 - 1 / p , 1 / 2 - 1 / 2 p ( ∂ Ω T ) revisited”

Decomposition of the weighted Sobolev space W 1 , p ( Ω , d M ϵ ) and its traces

The fractional dimensional theory in Lüroth expansion

Entire solutions in ℝ 2 for a class of Allen-Cahn equations

Computing powers of two generalizations of the logarithm.

Constructions of smooth and analytic cocycles over irrational circle rotations

Displaying similar documents to “The trace theorem $W_{p}^{2, 1} (Ω_{T}) ∋ f \mapsto \nabla_{x} f \in W_{p}^{1 - 1 / p, 1 / 2 - 1 / 2 p} (\partial Ω_{T})$ revisited”

Decomposition of the weighted Sobolev space $W^{1, p} (Ω, d_{M}^{ϵ})$ and its traces

Entire solutions in $ℝ^{2}$ for a class of Allen-Cahn equations