{"abstract":[{"lang":"eng","text":"We study weak solutions to mean curvature flow satisfying Young’s angle condition for general contact angles α ∈ (0, π). First, we construct BV solutions by using the Allen-Cahn approximation with boundary contact energy as proposed by Owen and Sternberg. Second, we prove the weak-strong uniqueness and stability for this solution concept. The main ingredient for both results is a relative energy, which can also be interpreted as a tilt excess. "}],"article_type":"original","language":[{"iso":"eng"}],"corr_author":"1","quality_controlled":"1","oa":1,"type":"journal_article","publication_identifier":{"issn":["0022-2518"]},"scopus_import":"1","external_id":{"arxiv":["2112.11150"]},"issue":"1","page":"111-148","volume":73,"publication_status":"published","OA_type":"green","doi":"10.1512/iumj.2024.73.9701","article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.11150","open_access":"1"}],"date_published":"2024-01-01T00:00:00Z","author":[{"full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel"},{"first_name":"Tim","full_name":"Laux, Tim","last_name":"Laux"}],"intvolume":"        73","department":[{"_id":"JuFi"}],"date_created":"2025-01-27T15:20:19Z","day":"01","citation":{"mla":"Hensel, Sebastian, and Tim Laux. “BV Solutions for Mean Curvature Flow with Constant Angle: Allen-Cahn Approximation and Weak-Strong Uniqueness.” <i>Indiana University Mathematics Journal</i>, vol. 73, no. 1, Indiana University Mathematics Journal, 2024, pp. 111–48, doi:<a href=\"https://doi.org/10.1512/iumj.2024.73.9701\">10.1512/iumj.2024.73.9701</a>.","ieee":"S. Hensel and T. Laux, “BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness,” <i>Indiana University Mathematics Journal</i>, vol. 73, no. 1. Indiana University Mathematics Journal, pp. 111–148, 2024.","chicago":"Hensel, Sebastian, and Tim Laux. “BV Solutions for Mean Curvature Flow with Constant Angle: Allen-Cahn Approximation and Weak-Strong Uniqueness.” <i>Indiana University Mathematics Journal</i>. Indiana University Mathematics Journal, 2024. <a href=\"https://doi.org/10.1512/iumj.2024.73.9701\">https://doi.org/10.1512/iumj.2024.73.9701</a>.","ama":"Hensel S, Laux T. BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness. <i>Indiana University Mathematics Journal</i>. 2024;73(1):111-148. doi:<a href=\"https://doi.org/10.1512/iumj.2024.73.9701\">10.1512/iumj.2024.73.9701</a>","short":"S. Hensel, T. Laux, Indiana University Mathematics Journal 73 (2024) 111–148.","apa":"Hensel, S., &#38; Laux, T. (2024). BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness. <i>Indiana University Mathematics Journal</i>. Indiana University Mathematics Journal. <a href=\"https://doi.org/10.1512/iumj.2024.73.9701\">https://doi.org/10.1512/iumj.2024.73.9701</a>","ista":"Hensel S, Laux T. 2024. BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness. Indiana University Mathematics Journal. 73(1), 111–148."},"month":"01","year":"2024","publisher":"Indiana University Mathematics Journal","title":"BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness","OA_place":"repository","arxiv":1,"_id":"18926","publication":"Indiana University Mathematics Journal","oa_version":"Preprint","status":"public","date_updated":"2025-01-27T15:23:57Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}