{"month":"02","article_type":"original","status":"public","abstract":[{"lang":"eng","text":"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 &gt; 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))."}],"keyword":["General Mathematics"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":131,"language":[{"iso":"eng"}],"citation":{"ieee":"M. Moser, “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,” <i>Asymptotic Analysis</i>, vol. 131, no. 3–4. IOS Press, pp. 297–383, 2023.","ista":"Moser M. 2023. 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. Asymptotic Analysis. 131(3–4), 297–383.","ama":"Moser M. 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. <i>Asymptotic Analysis</i>. 2023;131(3-4):297-383. doi:<a href=\"https://doi.org/10.3233/asy-221775\">10.3233/asy-221775</a>","apa":"Moser, M. (2023). 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. <i>Asymptotic Analysis</i>. IOS Press. <a href=\"https://doi.org/10.3233/asy-221775\">https://doi.org/10.3233/asy-221775</a>","chicago":"Moser, Maximilian. “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.” <i>Asymptotic Analysis</i>. IOS Press, 2023. <a href=\"https://doi.org/10.3233/asy-221775\">https://doi.org/10.3233/asy-221775</a>.","short":"M. Moser, Asymptotic Analysis 131 (2023) 297–383.","mla":"Moser, Maximilian. “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.” <i>Asymptotic Analysis</i>, vol. 131, no. 3–4, IOS Press, 2023, pp. 297–383, doi:<a href=\"https://doi.org/10.3233/asy-221775\">10.3233/asy-221775</a>."},"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","article_processing_charge":"No","publication":"Asymptotic Analysis","type":"journal_article","date_published":"2023-02-02T00:00:00Z","date_updated":"2025-09-09T14:14:55Z","author":[{"full_name":"Moser, Maximilian","last_name":"Moser","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","first_name":"Maximilian"}],"publisher":"IOS Press","year":"2023","day":"02","oa_version":"Preprint","scopus_import":"1","external_id":{"arxiv":["2105.07100"],"isi":["000927801300001"]},"issue":"3-4","_id":"14755","acknowledgement":"The author gratefully acknowledges support through DFG, GRK 1692 “Curvature,\r\nCycles and Cohomology” during parts of the work.","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.07100"}],"isi":1,"date_created":"2024-01-08T13:13:28Z","publication_identifier":{"eissn":["1875-8576"],"issn":["0921-7134"]},"department":[{"_id":"JuFi"}],"intvolume":"       131","quality_controlled":"1","corr_author":"1","publication_status":"published","page":"297-383","arxiv":1,"doi":"10.3233/asy-221775"}