Displaying similar documents to “A compactness theorem of n-harmonic maps”

On weighted spaces of functions harmonic in ℝ n

Albert I. Petrosyan (2006)

Commentationes Mathematicae Universitatis Carolinae

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The paper establishes integral representation formulas in arbitrarily wide Banach spaces b ω p ( ℝ n ) of functions harmonic in the whole ℝ n .

Fractional integro-differentiation in harmonic mixed norm spaces on a half-space

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 h ( p , q , α ) 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 h ( p , q , α ) for the range 0 < p ≤ ∞ , 0 < q ≤ ∞ . As an application of the above, we give a characterization of h ( p , q , α ) by means of an integral representation with the use of Besov spaces.

About steady transport equation I – L p -approach in domains with smooth boundaries

Antonín Novotný (1996)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the steady transport equation λ z + w · ∇ z + a z = f , λ > 0 in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions w , a are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular stress is put onto the problem to extend the results to as less regular vector fields w , a , as possible (conserving the requirement...