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Hausdorff dimension of singular sets of Sobolev functions and maximally singular Sobolev functions

In this invited lecture presented at the Mathematics department of the Czech Academy of Sciences (upon invitation of prof.dr. Milan Kucera), recent results of the author were presented concerning optimal estimates of Hausdorff dimension of singular sets of functions in various spaces of functions, in particular from Sobolev spaces. Methods of proof were described, involving fractal analysis (box dimension, Minkowski content, Bessel potentials, etc).

Sobolev space; Hausdorff dimension; box dimension; Minkowski content

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