Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets

Bartłomiej Dyda

Displaying similar documents to “Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets”

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Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Adam Parusiński (2005)

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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.

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Marco Annoni, Emanuele Casini (2007)

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F. J. Pérez (2005)

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Anisotropic Lipschitz spaces are considered. For these spaces we obtain sharp embeddings in Besov and Lorentz spaces. The methods used are based on estimates of iterative rearrangements. We find a unified approach that arises from the estimation of functions defined as minimum of a given system of functions. The case of L¹-norm is also covered.

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Björn E. J. Dahlberg, C. E. Kenig, G. C. Verchota (1986)

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In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator $Δ^{2}$ , on an arbitrary bounded Lipschitz domain $D$ in $R^{n}$ . We establish existence and uniqueness results when the boundary values have first derivatives in $L^{2} (\partial D)$ , and the normal derivative is in $L^{2} (\partial D)$ . The resulting solution $u$ takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of $\nabla u$ is shown to be in $L^{2} (\partial D)$ .

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