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A diffused interface with the advection term in a Sobolev space

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arxiv 1904.00525 v2 pith:EARMLM26 submitted 2019-04-01 math.AP

Yoshihiro Tonegawa , Yuki Tsukamoto This is my paper · ORCID
classification math.AP
keywords advectiontermcurvaturediffusedenergyinterfacelimitmean
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We study the asymptotic limit of diffused surface energy in the van der Waals--Cahn--Hillard theory when an advection term is added and the energy is uniformly bounded. We prove that the limit interface is an integral varifold and the generalized mean curvature vector is determined by the advection term. As the application, a prescribed mean curvature problem is solved using the min-max method.

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  1. The Dirichlet problem for a prescribed mean curvature equation

    math.AP 2019-08 conditional novelty 6.0 of 10

    For prescribed mean curvature equations with a small W^{1,p} forcing term and small boundary data, a W^{2,q} solution exists near any given graphical minimal surface.

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