Calculus of Variations and Geometric Measure Theory

F. Giannetti - A. Passarelli di Napoli

Isoperimetric type inequalities for differential forms on manifolds

created by passarell on 09 Dec 2005


Published Paper

Inserted: 9 dec 2005

Journal: Indiana University Math. Journal
Volume: 54
Number: 5
Pages: 1483-1498
Year: 2005


Let $X$ be a smooth oriented Riemannian $n$-manifold without boundary and $(\Phi,\Psi)\in {\cal L}^p(\wedge ^l X)\times {\cal L}^r(\wedge ^{n-l} X)$ ,$\frac {1}{p}+\frac {1}{r}=1+\frac {1}{n}$ , 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 Hölder continuity for solutions of Hodge systems.