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Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis

Maria Alessandra Ragusa (1999)

Commentationes Mathematicae Universitatis Carolinae

In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class H 0 1 , p ( Ω ) for all 1 < p < and, as a consequence, the Hölder regularity of the solution u . is an elliptic second order operator with discontinuous coefficients ( V M O ) and the lower order terms belong to suitable Lebesgue spaces.

Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold

Vladimir A. Mikhailets, Aleksandr A. Murach (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.

Embedding theorems for anisotropic Lipschitz spaces

F. J. Pérez (2005)

Studia Mathematica

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.

Embeddings of Besov spaces of logarithmic smoothness

Fernando Cobos, Óscar Domínguez (2014)

Studia Mathematica

This paper deals with Besov spaces of logarithmic smoothness B p , r 0 , b formed by periodic functions. We study embeddings of B p , r 0 , b into Lorentz-Zygmund spaces L p , q ( l o g L ) β . Our techniques rely on the approximation structure of B p , r 0 , b , Nikol’skiĭ type inequalities, extrapolation properties of L p , q ( l o g L ) β and interpolation.

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