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.

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Attribution 4.0 International

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