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Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
Growth rates, Hausdorff measure and stability for the p-obstacle problem(3/2≤p≤2)
growth rate Hausdorff measure obstacle problem stability
2011/10/17
In this paper, we consider the free boundary for the inho-mogeneous obstacle problem with zero obstacle. We firstly establish the growth rates for the solution u(x) and the gradient of u(x), awa...