Trace maps for rough hypersurfaces in Sobolev spaces.
In this paper we revisit the problem of bounded trace maps on hypersurfaces, for Sobolev spaces. We look to this problem from a point of view that is fundamentally different from the one in the classical theory of trace maps. In this way, we construct bounded trace maps on rough hypersurfaces, for Sobolev spaces, under weak assumptions on the regularity of the hypersurfaces. Furthermore, using our trace maps we prove a coarea formula where the level sets are rough hypersurfaces that satisfy weak regularity assumptions.
Publisher URL: http://arxiv.org/abs/1810.06094