Isoperimetric inequality for div-curl fields

Abstract

Let be a Hölder conjugate pair of vector fields, both belonging to the space . Suppose that div and curl . In this paper we prove the following isoperimetric type inequality where and . As an application, we recover Hölder continuity for solutions of n-Laplace equation .

Keywords

• Isoperimetric inequality
• Div-curl fields
• Hölder continuity