{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:52Z","timestamp":1777447912186,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2018,8,3]],"date-time":"2018-08-03T00:00:00Z","timestamp":1533254400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,8,3]]},"abstract":"<jats:p>We investigate the qualitative properties of solutions to the Zaremba type problem in unbounded domains for non-divergence elliptic equation with possible degeneration at infinity. The main result is a Phragm\u00e9n\u2013Lindel\u00f6f type principle on growth\/decay of a solution at infinity depending on both the structure of the Neumann portion of the boundary and the \u201cthickness\u201d of its Dirichlet portion. The result is formulated in terms of the so-called s-capacity of the Dirichlet portion of the boundary, while the Neumann boundary should satisfy certain \u201cadmissibility\u201d condition in the sequence of layers converging to infinity.<\/jats:p>","DOI":"10.3233\/asy-181469","type":"journal-article","created":{"date-parts":[[2018,9,18]],"date-time":"2018-09-18T15:47:45Z","timestamp":1537285665000},"page":"75-90","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Mixed boundary value problems for non-divergence type elliptic equations in\u00a0unbounded domains"],"prefix":"10.1177","volume":"109","author":[{"given":"Dat","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX\u00a079409-1042, USA. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akif","family":"Ibraguimov","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX\u00a079409-1042, USA. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander I.","family":"Nazarov","sequence":"additional","affiliation":[{"name":"St. Petersburg Department of Steklov Institute, Fontanka 27, St. Petersburg, 191023, Russia"},{"name":"St. Petersburg State University, Universitetskii pr. 28, St. Petersburg, 198504, Russia. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,8,3]]},"reference":[{"issue":"6","key":"ref001","first-page":"1073","volume":"6","author":"Abbasov A.T.","year":"1970","journal-title":"Differ. 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