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.