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We examine how Poincaré change under quasiconformal maps between appropriate metric spaces having the same Hausdorff dimension. We also show that for many metric spaces the Sobolev functions can be identified with functions satisfying Poincaré, and this allows us to extend to the metric space setting the fact that quasiconformal maps from $ℝ^{Q}$ onto $ℝ^{Q}$ preserve the Sobolev space $L^{1, Q} (ℝ^{Q})$ .

Quasiconformal mappings with Sobolev boundary values

Kari Astala, Mario Bonk, Juha Heinonen (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider quasiconformal mappings in the upper half space $ℝ_{+}^{n + 1}$ of $ℝ^{n + 1}$ , $n \geq 2$ , whose almost everywhere defined trace in $ℝ^{n}$ has distributional differential in $L^{n} (ℝ^{n})$ . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space $H^{1}$ . More generally, we consider certain positive functions defined on $ℝ_{+}^{n + 1}$ , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them....

Quelques méthodes d'étude de la propagation d'oscillations hyperboliques non linéaires

D. Serre (1990/1991)

Séminaire Équations aux dérivées partielles (Polytechnique)

Quelques résultats sur les problèmes aux limites en théorie des distributions

Giuseppe Geymonat (1972)

Mémoires de la Société Mathématique de France

Radial Subspaces of Besov and Lizorkin-Triebel Classes: Extended Strauss Lemma and Compactness of Embeddings.

Winfried Sickel, Leszek Skrzypczak (2000)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Radial variation of functions in Besov spaces.

David Walsh (2006)

Publicacions Matemàtiques

Random fixed points for a certain class of asymptotically regular mappings

Balwant Singh Thakur, Jong Soo Jung, Daya Ram Sahu, Yeol Je Cho (1998)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let (Ω, σ) be a measurable space and K a nonempty bounded closed convex separable subset of a p-uniformly convex Banach space E for p > 1. We prove a random fixed point theorem for a class of mappings T:Ω×K ∪ K satisfying the condition: For each x, y ∈ K, ω ∈ Ω and integer n ≥ 1, ⃦Tⁿ(ω,x) - Tⁿ(ω,y) ⃦ ≤ aₙ(ω)· ⃦x - y ⃦ + bₙ(ω) ⃦x -Tⁿ(ω,x) ⃦ + ⃦y - Tⁿ(ω,y) ⃦ + cₙ(ω) ⃦x - Tⁿ(ω,y) ⃦ + ⃦y - Tⁿ(ω,x) ⃦, where aₙ, bₙ, cₙ: Ω → [0, ∞) are functions satisfying certain conditions and Tⁿ(ω,x) is the value...

Rational Approximation and Weak Analyticity. I.

Anthony G. O'Farrell (1985/1986)

Mathematische Annalen

Recent developments in the theory of function spaces

Triebel, Hans (1986)

Equadiff 6

Recent developments in the theory of function spaces with dominating mixed smoothness

Schmeisser, Hans-Jürgen (2007)

Nonlinear Analysis, Function Spaces and Applications

The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...

Régularité de la solution d’une équation fortement (ou faiblement) non linéaire dans $𝐑^{n}$

François de Thélin (1980)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Régularité de la solution forte de problèmes non linéaires d'évolution

Maria Giovanna Garroni, Maria Agostina Vivaldi (1979)

Czechoslovak Mathematical Journal

Régularité du temps local brownien dans les espaces de Besov-Orlicz

B. Boufoussi (1996)

Studia Mathematica

Let $(B_{t}, t \geq 0)$ be a linear Brownian motion and (L(t,x), t > 0, x ∈ ℝ) its local time. We prove that for all t > 0, the process (L(t,x), x ∈ [0,1]) belongs almost surely to the Besov-Orlicz space $B_{M_{1}, \infty}^{1 / 2}$ with $M_{1} (x) = e^{| x |} - 1$ .

Regularity and Decay of Eigenfunctions.

Werner Stork (1978)

Mathematische Zeitschrift

Regularity for a clamped grid equation $u_{x x x x} + u_{y y y y} = f$ on a domain with a corner.

Gerasimov, Tymofiy, Sweers, Guido (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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