Let X be a smooth oriented Riemannian n-manifold without boundary and (Phi, Psi) is an element of L-p (Lambda^(l) X) x L-r(Lambda^(n-l)X), 1/p + 1/r = 1 + 1/n, be a pair of closed differential forms. We prove an isoperimetric type inequality for such differential forms under suitable assumptions. As an application we derive Holder continuity for solutions of Hodge systems.
ISOPERIMETRIC TYPE INEQUALITIES FOR DIFFERENTIAL FORMS ON MANIFOLDS / Giannetti, Flavia; PASSARELLI DI NAPOLI, Antonia. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 54:5(2005), pp. 1483-1497. [10.1512/iumj.2005.54.2665]
ISOPERIMETRIC TYPE INEQUALITIES FOR DIFFERENTIAL FORMS ON MANIFOLDS
GIANNETTI, FLAVIA;PASSARELLI DI NAPOLI, ANTONIA
2005
Abstract
Let X be a smooth oriented Riemannian n-manifold without boundary and (Phi, Psi) is an element of L-p (Lambda^(l) X) x L-r(Lambda^(n-l)X), 1/p + 1/r = 1 + 1/n, be a pair of closed differential forms. We prove an isoperimetric type inequality for such differential forms under suitable assumptions. As an application we derive Holder continuity for solutions of Hodge systems.File in questo prodotto:
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