Jan Maly, Department of Mathematics, MFF UK.
"Fine properties of Sobolev-Orlicz functions and the coarea formula"
For a special class of Young functions, the Sobolev-Orlicz capacity is estimated from below by the (n-m)-dimensional Hausdorff content. The proof is based on pointwise estimates of superminimizers of the Orlicz type Dirichlet integrals. As a consequence we derive a sharp answer to the question which Sobolev functions have Lebesgue points Hn-m-a.e. and serve as good transformations for the coarea change of variables.
In part a joint work with D. Swanson and W. P. Ziemer.
THURSDAY, March 14, 2002