*Published Paper*

**Inserted:** 9 dec 2005

**Journal:** Indiana University Math. Journal

**Volume:** 54

**Number:** 5

**Pages:** 1483-1498

**Year:** 2005

**Abstract:**

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 HÃ¶lder continuity for solutions of Hodge systems.

**Download:**