On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content
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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 Lp norm of derivative of solutions is given.
CitationKorkut, 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. Electronic Journal of Differential Equations, 2007(37), pp. 1-21.
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