engleski

On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content

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.

double obstacles ; nonlinear p-Laplacian ; graph

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