Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 37, pp. 1-21.

Title: On a class of nonlinear variational inequalities:
       High concentration of the graph of weak solution via its
       fractional dimension and Minkowski content

Authors: Luka Korkut  (Univ. of Zagreb, Croatia)
         Mervan Pasic (Univ. of Zagreb, Croatia)
 
Abstract:
 Weak continuous bounded solutions of a class of nonlinear
 variational inequalities associated to one-dimensional
 p-Laplacian are studied. It is shown that a kind of boundary
 behaviour of nonlinearity in the main problem produces a kind of
 high boundary concentration of the graph of solutions. It is
 verified by calculating lower bounds for the upper
 Minkowski-Bouligand dimension and Minkowski content of the graph
 of each solution and its derivative. Finally, the order of growth
 for singular behaviour of the $L^{p}$ norm of derivative of
 solutions is given.
  
Submitted November 19, 2006. Published March 1, 2007.
Math Subject Classifications: 35J85, 34B15, 28A75.
Key Words: Double obstacles; nonlinear p-Laplacian; graph; 
           fractional dimension; Minkowski content; 
	   singularity of derivative.