ar X iv : 0 70 7 . 03 76 v 1 [ m at h . FA ] 3 J ul 2 00 7 SELF IMPROVING SOBOLEV - POINCARÉ INEQUALITIES , TRUNCATION AND SYMMETRIZATION
نویسنده
چکیده
In our recent paper [12] we developed a new principle of “symmetrization by truncation” to obtain symmetrization inequalities of Sobolev type via truncation. In this note we consider the corresponding results for Sobolev spaces on domains, without assuming that the Sobolev functions vanish at the boundary. The explicit connection between Sobolev-Poincaré inequalities and isoperimetric inequalities appears in the work of Maz’ya. In [13] it is shown that if Ω ⊂ R is an arbitrary open set with finite volume, 1 ≤ p ≤ n/(n−1), then the Sobolev-Poincaré
منابع مشابه
Sobolev Inequalities: Symmetrization and Self Improvement via Truncation
We develop a new method to obtain symmetrization inequalities of Sobolev type. Our approach leads to new inequalities and considerable simplification in the theory of embeddings of Sobolev spaces based on rearrangement invariant spaces.
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