a stability result for p-harmonic systems with discontinuous coefficients
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ID: 249599
2001
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Abstract
The present paper is concerned with p-harmonic systems $$ mathop{ m div} (langle A(x) Du(x), Du(x) angle ^{{p-2}over 2} A(x) Du(x))=mathop{ m div} ( sqrt{A(x)} F(x)),$$ where $A(x)$ is a positive definite matrix whose entries have bounded mean oscillation (BMO), $p$ is a real number greater than 1 and $Fin L^{rover {p-1}}$ 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.
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stroffolini2001electronica
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| Authors | ;Bianca Stroffolini |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2001 |
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