On embeddings, traces and multipliers in harmonic function spaces
Miloš Arsenović, Romi F. Shamoyan (2013)
Kragujevac Journal of Mathematics
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Miloš Arsenović, Romi F. Shamoyan (2013)
Kragujevac Journal of Mathematics
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Karen L. Avetisyan (2001)
Commentationes Mathematicae Universitatis Carolinae
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In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces on the half-space are established. We prove that mixed norm is equivalent to a “fractional derivative norm” and that harmonic conjugation is bounded in for the range , . As an application of the above, we give a characterization of by means of an integral representation with the use of Besov spaces.
A. Bonilla (2000)
Colloquium Mathematicae
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We prove that, if μ>0, then there exists a linear manifold M of harmonic functions in which is dense in the space of all harmonic functions in and lim‖x‖→∞ x ∈ S ‖x‖μDαv(x) = 0 for every v ∈ M and multi-index α, where S denotes any hyperplane strip. Moreover, every nonnull function in M is universal. In particular, if μ ≥ N+1, then every function v ∈ M satisfies ∫H vdλ =0 for every (N-1)-dimensional hyperplane H, where λ denotes the (N-1)-dimensional Lebesgue measure. On the other...
Jan W. Cholewa, Aníbal Rodríguez-Bernal (2014)
Mathematica Bohemica
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We consider the Cahn-Hilliard equation in with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as and logistic type nonlinearities. In both situations we prove the -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).
Chang You Wang (2005)
Annales de l'I.H.P. Analyse non linéaire
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