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.