2022-05-20T20:05:08Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/695192018-04-25T23:44:09Zhdl_2115_45007hdl_2115_116Diffused interface with the chemical potential in the Sobolev spaceTonegawa, Yoshihiro410We 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 W1,p of the associated chemical potential fields are bounded uniformly, where p > n 2 and n is the dimension of the domain. We show that the limit interface as ε tending to zero is an integral varifold with the sharp integrability condition on the mean curvature.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69519info:doi/10.14943/83865https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69519/1/pre714.pdfHokkaido University Preprint Series in Mathematics7141232005engpublisher