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Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1007\/s40314-023-02210-3","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T13:03:44Z","timestamp":1675688624000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Filling holes under non-linear constraints"],"prefix":"10.1007","volume":"42","author":[{"given":"A. L.","family":"Cust\u00f3dio","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8418-8490","authenticated-orcid":false,"given":"M. A.","family":"Fortes","sequence":"additional","affiliation":[]},{"given":"A. 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