Electron. J. Diff. Eqns., Vol. 2002(2002), No. 20, pp. 1-13.

${\cal L}^{2,\Phi}$ regularity for nonlinear elliptic systems of second order

Josef Danecek & Eugen Viszus

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.

Submitted May 31, 2001. Published February 19, 2002.
Math Subject Classifications: 49N60, 35J60.
Key Words: Nonlinear equations, regularity, Morrey-Campanato spaces.

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Josef Danecek
Department of Mathematics,
Faculty of Civil Engineering,
Zizkova 17, 60200 Brno, Czech Republic
e-mail: danecek.j@fce.vutbr.cz
Eugen Viszus
Department of Mathematical Analysis,
Faculty of Mathematics and Physics,
Comenius University, Mlynska dolina,
84248 Bratislava, Slovak Republic
e-mail: Eugen.Viszus@fmph.uniba.sk

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