On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content
Date
2007-03-01
Authors
Korkut, Luka
Pasic, Mervan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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<sup>p</sup> norm of derivative of solutions is given.
Description
Keywords
Double obstacles, Nonlinear p-Laplacian, Graph, Fractional dimension, Minkowski content, Singularity of derivative
Citation
Korkut, L., & Pasic, M. (2007). On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content. <i>Electronic Journal of Differential Equations, 2007</i>(37), pp. 1-21.
Rights
Attribution 4.0 International