## Differential and Integral Equations

### A compactness result for $p$-harmonic maps

Patrick Courilleau

#### Abstract

For $p>1$ we prove a compactness result for $p$-harmonic maps with values in $S^k$, the $(k+1)$-dimensional sphere. We generalize a lemma from [12] to vector-valued functions with assumptions on the $p$-Laplacian. We obtain the existence of weak solutions of the $p$-harmonic flow with values in $S^k$ for each $k\geq 1$ and $p>1$.

#### Article information

Source
Differential Integral Equations, Volume 14, Number 1 (2001), 75-84.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356123376

Mathematical Reviews number (MathSciNet)
MR1797933

Zentralblatt MATH identifier
1021.35006

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35A25: Other special methods

#### Citation

Courilleau, Patrick. A compactness result for $p$-harmonic maps. Differential Integral Equations 14 (2001), no. 1, 75--84. https://projecteuclid.org/euclid.die/1356123376