---
res:
  bibo_abstract:
  - We consider the sharp interface limit for the scalar-valued and vector-valued
    Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth
    domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse
    interface has developed and intersects the boundary ∂ Ω. The limit problem is
    mean curvature flow with 90°-contact angle and we show convergence in strong norms
    for well-prepared initial data as long as a smooth solution to the limit problem
    exists. To this end we assume that the limit problem has a smooth solution on
    [ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear
    coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued
    Allen–Cahn equation. In order to estimate the difference of the exact and approximate
    solutions with a Gronwall-type argument, a spectral estimate for the linearized
    Allen–Cahn operator in both cases is required. The latter will be shown in a separate
    paper, cf. (Moser (2021)).@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Maximilian
      foaf_name: Moser, Maximilian
      foaf_surname: Moser
      foaf_workInfoHomepage: http://www.librecat.org/personId=a60047a9-da77-11eb-85b4-c4dc385ebb8c
  bibo_doi: 10.3233/asy-221775
  bibo_issue: 3-4
  bibo_volume: 131
  dct_date: 2023^xs_gYear
  dct_identifier:
  - UT:000927801300001
  dct_isPartOf:
  - http://id.crossref.org/issn/0921-7134
  - http://id.crossref.org/issn/1875-8576
  dct_language: eng
  dct_publisher: IOS Press@
  dct_subject:
  - General Mathematics
  dct_title: 'Convergence of the scalar- and vector-valued Allen–Cahn equation to
    mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence
    result@'
...