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.
@article{ASNSP_2005_5_4_3_487_0, author = {Tonegawa, Yoshihiro}, title = {A diffused interface whose chemical potential lies in a {Sobolev} space}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {487--510}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 4}, number = {3}, year = {2005}, mrnumber = {2185866}, zbl = {1170.35416}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2005_5_4_3_487_0/} }
TY - JOUR AU - Tonegawa, Yoshihiro TI - A diffused interface whose chemical potential lies in a Sobolev space JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2005 SP - 487 EP - 510 VL - 4 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2005_5_4_3_487_0/ LA - en ID - ASNSP_2005_5_4_3_487_0 ER -
%0 Journal Article %A Tonegawa, Yoshihiro %T A diffused interface whose chemical potential lies in a Sobolev space %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2005 %P 487-510 %V 4 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2005_5_4_3_487_0/ %G en %F ASNSP_2005_5_4_3_487_0
Tonegawa, Yoshihiro. A diffused interface whose chemical potential lies in a Sobolev space. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 3, pp. 487-510. http://archive.numdam.org/item/ASNSP_2005_5_4_3_487_0/
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