Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 02, pp. 1-7.
Title: A stability result for p-harmonic systems with discontinuous coefficients
Author: Bianca Stroffolini (R. Caccioppoli, Napoli, Italy)
Abstract:
The present paper is concerned with p-harmonic systems
$$ \mathop{\rm div} (\langle A(x) Du(x), Du(x) \rangle ^{{p-2}\over 2} A(x)
Du(x))=\mathop{\rm div} ( \sqrt{A(x)} F(x)),$$
where $A(x)$ is a positive definite matrix whose entries have
bounded mean oscillation (BMO),
$p$ is a real number greater than 1 and $F\in L^{r\over {p-1}}$
is a given matrix field.
We find a-priori estimates for a very weak solution of class $W^{1,r}$,
provided $r$ is close to $2$, depending on the BMO norm of
$\sqrt{A}$, and p
close to $r$.
This result is achieved using the corresponding existence and
uniqueness result for linear systems with BMO coefficients
[St], combined with nonlinear commutators.
Submitted November 27, 2000. Published January 2, 2001.
Math Subject Classifications: 35J60, 47B47.
Key Words: Bounded mean oscillation; Linear and Nonlinear Commutators;
Hodge Decomposition.