Displaying similar documents to “A stability result for p -harmonic systems with discontinuous coefficients.”

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.

Caccioppoli estimates and very weak solutions of elliptic equations

Tadeusz Iwaniec, Carlo Sbordone (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Caccioppoli estimates are instrumental in virtually all analytic aspects of the theory of partial differential equations, linear and nonlinear. And there is always something new to add to these estimates. We emphasize the fundamental role of the natural domain of definition of a given differential operator and the associated weak solutions. However, we depart from this usual setting (energy estimates) and move into the realm of the so-called very weak solutions where important new applications...