We prove that for mappings in , continuous up to the boundary and with modulus of continuity satisfying a certain divergence condition, the image of the boundary of the unit ball has zero -Hausdorff measure. For Hölder continuous mappings we also prove an essentially sharp generalised Hausdorff dimension estimate.
"Boundary blow-up under Sobolev mappings." Anal. PDE 7 (8) 1839 - 1850, 2014. https://doi.org/10.2140/apde.2014.7.1839