Geodesic
A stability result for $p$-harmonic systems with discontinuous coefficients
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35J60, 47B47
Keywords: bounded mean oscillation, linear and nonlinear commutators, Hodge decomposition 
@article{EJDE_2001__2001__a161,
     author = {Stroffolini, Bianca},
     title = {A stability result for $p$-harmonic systems with discontinuous coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a161/}
}
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Stroffolini, Bianca. A stability result for $p$-harmonic systems with discontinuous coefficients. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a161/