{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:01:47Z","timestamp":1760151707722,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T00:00:00Z","timestamp":1649721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>First, we prove that the BMO condition by John\u2013Nirenberg leads in the natural way to the asymptotic homogeneity at the origin of regular homeomorphic solutions of the degenerate Beltrami equations. Then, on this basis we establish a series of criteria for the existence of regular homeomorphic solutions of the degenerate Beltrami equations in the whole complex plane with asymptotic homogeneity at infinity. These results can be applied to the fluid mechanics in strongly anisotropic and inhomogeneous media because the Beltrami equation is a complex form of the main equation of hydromechanics.<\/jats:p>","DOI":"10.3390\/axioms11040171","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T21:15:35Z","timestamp":1649798135000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["BMO and Asymptotic Homogeneity"],"prefix":"10.3390","volume":"11","author":[{"given":"Vladimir","family":"Gutlyanskii","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 84100 Slavyansk, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Ryazanov","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 84100 Slavyansk, Ukraine"},{"name":"Laboratory of Mathematical Physics, Department of Physics, Bogdan Khmelnytsky National University of Cherkasy, 18031 Cherkasy, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7892-6186","authenticated-orcid":false,"given":"Evgeny","family":"Sevost\u2019yanov","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 84100 Slavyansk, Ukraine"},{"name":"Department of Mathematical Analysis, Business Analysis and Statistics, Zhytomyr Ivan Franko State University, 10008 Zhytomyr, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduard","family":"Yakubov","sequence":"additional","affiliation":[{"name":"H.I.T. Holon Institute of Technology, Holon 5810201, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1002\/cpa.3160140317","article-title":"On functions of bounded mean oscillation","volume":"14","author":"John","year":"1961","journal-title":"Comm. Pure Appl. Math."},{"key":"ref_2","unstructured":"Heinonen, J., Kilpelainen, T., and Martio, O. (1993). Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Clarendon Press."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Reimann, H.M., and Rychener, T. (1975). Funktionen Beschr\u00e4nkter Mittlerer Oscillation, Springer. 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