Geodesic
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, Tome 2007 (2007)
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.
Classification : 35J85, 34B15, 28A75
Keywords: double obstacles, nonlinear p-Laplacian, graph, fractional dimension, Minkowski content, singularity of derivative 
@article{EJDE_2007__2007__a178,
     author = {Korkut,  Luka and Pa\v{s}i\'c,  Mervan},
     title = {On a class of nonlinear variational inequalities: high concentration of the graph of weak solution via its fractional dimension and {Minkowski} content},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1189.35138},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a178/}
}
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Korkut,  Luka; Pašić,  Mervan. 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, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a178/