Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 14, pp. 1-14.

Title: A class of nonlinear elliptic variational inequalities:
       qualitative properties and existence of solutions
   
Authors: Luka Korkut (Univ. of Zagreb,  Croatia)
  Mervan Pasic (Univ. of Zagreb,  Croatia)
  Darko Zubrinic (Univ. of Zagreb,  Croatia)


Abstract:  
  We study a class of nonlinear elliptic variational inequalities 
 in divergence  form. In the recent paper [6], we obtained
 results on the local control of essential infimum and supremum of
 solutions of quasilinear elliptic equations, and here we extend this
 point of view to the case of variational inequalities.
 It implies a new qualitative property of solutions in $W^{1,p}(\Omega )$
 which we call ``jumping over the control obstacle.''
 Using the Schwarz symmetrization technique, we give an existence
 and symmetrization theorems in
 $W_0^{1,p}(\Omega )\cap L^{\infty }(\Omega )$
 which agree completely with previous qualitative results. Also we consider
 generating singularities of weak solutions in $W^{1,p}(\Omega )$
 of variational inequalities. 
 
Submitted December 15, 2001. Published February 9, 2002.
Math Subject Classifications: 35J65, 35J85, 35B05.
Key Words: variational inequalities; double obstacle; 
           qualitative properties; Schwarz symmetrization; 
           generating singularities.