Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 20, pp. 1-13.
Title: $L^{2,\Phi}$ regularity for nonlinear elliptic systems
of second order
Authors: Josef Danecek (Faculty of Civil Engineering, Czech Republic)
Eugen Viszus (Comenius Univ., Mlynska dolina, Slovak Republic)
Abstract:
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 $L^\infty(\Omega)\cap\mathcal{L}^{2,\varPsi}(\Omega)$
(generalized Campanato spaces),
then the gradient of the weak solutions belong to
$\mathcal{L}_{loc}^{2,\varPhi}(\Omega,\mathbb{R}^{nN})$,
where the relation between the functions
$\varPsi$ and $\varPhi$ 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.