Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 60, pp. 1-25.
Title: Some metric-singular properties of the graph of solutions
of the one-dimensional p-Laplacian
Authors: Mervan Pasic (Univ. of Zagreb, Croatia)
Vesna Zupanovic (Univ. of Zagreb, Croatia)
Abstract:
We study the asymptotic behaviour of $epsilon$-neighbourhood
of the graph of a type of rapidly oscillating continuous functions.
Next, we estate necessary and sufficient conditions for rapid
oscillations of solutions of the main equation. This enables us
to verify some new singular properties of bounded continuous
solutions of a class of nonlinear p-Laplacian by calculating
lower and upper bounds for the Minkowski content and the
$s$-dimensional density of the graph of each solution and
its derivative.
Submitted October 28, 2003. Published April 19, 2004.
Math Subject Classifications: 35J60, 34B15, 28A75.
Key Words: Nonlinear p-Laplacian; bounded solutions; qualitative properties;
graph; singularity; Minkowski content; s-dimensional density.