A generalization of the Gagliardo inequality |
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Authors: | D. V. Maksimov |
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Affiliation: | (1) Russian State Pedagogical University, St.Petersburg, Russia |
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Abstract: | Consider functions u1, u2,..., un ∈ D(ℝk) and assume that we are given a certain set of linear combinations of the form ∑i, j a ij (l) ∂jui. Sufficient conditions in terms of coefficients a ij (l) are indicated under which the norms are controlled in terms of the L1-norms of these linear combinations. These conditions are mostly transparent if k = 2. The classical Gagliardo inequality corresponds to a single function u1 = u and the collection of its partial derivatives ∂1u,..., ∂ku. Bibliography: 2 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 120–139. |
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