Geodesic
${\cal L}^{2,\Phi}$ regularity for nonlinear elliptic systems of second order
Electronic Journal of Differential Equations, Tome 2002 (2002).

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

Summary: This paper is concerned with the regularity of the gradient of the weak solutions to nonlinear elliptic systems with linear main parts. It demonstrates the connection between the regularity of the (generally discontinuous) coefficients of the linear parts of systems and the regularity of the gradient of the weak solutions of systems. More precisely: If above-mentioned coefficients belong to the class $L^\infty(\Omega)\cap{\cal L}^{2,\Psi}(\Omega)$ (generalized Campanato spaces), then the gradient of the weak solutions belong to ${\cal L}_{loc}^{2,\Phi}(\Omega,\mathbb{R}^{nN})$, where the relation between the functions $\Psi$ and $\Phi$ is formulated in Theorems 3.1 and 3.2.
Classification : 49N60, 35J60
Keywords: nonlinear equations, regularity, Morrey-campanato spaces 
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     author = {Dan\v{e}\v{c}ek, Josef and Viszus, Eugen},
     title = {${\cal L}^{2,\Phi}$ regularity for nonlinear elliptic systems of second order},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a159/}
}
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Daněček, Josef; Viszus, Eugen. ${\cal L}^{2,\Phi}$ regularity for nonlinear elliptic systems of second order. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a159/