L^s-Estimates for the Solutions of A-Harmonic Equations and the Related Operators
by
Bing Liu
Saginaw Valley State University, University Center, MI 48710

We know that the p-harmonic equation div(∇u |∇u|^p-2) = 0 is a special case of the A-harmonic equation div  A (x, ∇u) = 0 for functions in Rⁿ, where A: Rⁿ×Rⁿ → Rⁿ is a mapping satisfying certain conditions. If u is a differential form, the above A-harmonic equation has the following more general version d^* A(x, du)=0, where d^* is the Hodge codifferential operator. The corresponding nonhomogeneous A-harmonic equation appears d^* A(x, du)=B(x, du). In this talk, we will develop some L^s-estimates for the differential forms satisfying the A-harmonic equations. We will also obtain some estimates for the operators applied to these forms.

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Date received: February 5, 2008