Existence an regularity of constant mean curvature hypersurfaces in hyperbolic space.
A diffused interface whose chemical potential lies in a Sobolev space
We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms of the associated chemical potential fields are bounded uniformly, where and is the dimension of the domain. We show that the limit interface as tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.
Partial Regulartiy for Evolution Problems with Discontinuity.
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