Obstacle problems in variable exponent Sobolev spaces
 
 
Description: 

We are going to discuss the obstacle problem for a quite large class of heterogeneous quasi-linear degenerate elliptic operators in variable exponent Sobolev spaces (Orlicz-Sobolev spaces). We see that the solution has C^{1,\alpha}_{loc} regularity for some \alpha\in (0,1) and prove that the free boundary is a porous set, and hence has Lebesgue measure zero. For a speci fic class of operators we prove the finit eness of the (n-1) dimensional Hausdor ff measure of the free boundary.

If time allows, a model of a steady glacier flow also will be discussed. We represent the case as an obstacle problem in Orlicz-Sobolev spaces - with the corresponding equation being a fully nonlinear PDE. We show the existence of a solution using a fixed point argument.

Date:  2013-10-18
Start Time:   14:30
Speaker:  Rafayel Teymurazyan (CMAF, Univ. Lisboa)
Institution:  CMAF, Universidade de Lisboa
Place:  Sala 5.5
Research Groups: -Analysis
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