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...
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Texas State University
2007-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/37/abstr.html |
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doaj-ce59eeda090041f986aa8d8808f0dee42020-11-24T21:36:23ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-03-01200737121On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski contentMervan PasicLuka KorkutWeak 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.http://ejde.math.txstate.edu/Volumes/2007/37/abstr.htmlDouble obstaclesnonlinear p-Laplaciangraphfractional dimensionMinkowski contentsingularity of derivative. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mervan Pasic Luka Korkut |
| spellingShingle |
Mervan Pasic Luka Korkut 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 Double obstacles nonlinear p-Laplacian graph fractional dimension Minkowski content singularity of derivative. |
| author_facet |
Mervan Pasic Luka Korkut |
| author_sort |
Mervan Pasic |
| title |
On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content |
| title_short |
On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content |
| title_full |
On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content |
| title_fullStr |
On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content |
| title_full_unstemmed |
On a class of nonlinear variational inequalities: High concentration of the graph of weak solution via its fractional dimension and Minkowski content |
| title_sort |
on a class of nonlinear variational inequalities: high concentration of the graph of weak solution via its fractional dimension and minkowski content |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2007-03-01 |
| description |
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. |
| topic |
Double obstacles nonlinear p-Laplacian graph fractional dimension Minkowski content singularity of derivative. |
| url |
http://ejde.math.txstate.edu/Volumes/2007/37/abstr.html |
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AT mervanpasic onaclassofnonlinearvariationalinequalitieshighconcentrationofthegraphofweaksolutionviaitsfractionaldimensionandminkowskicontent AT lukakorkut onaclassofnonlinearvariationalinequalitieshighconcentrationofthegraphofweaksolutionviaitsfractionaldimensionandminkowskicontent |
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