Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)32665ArticlesСтатьиResearch ArticleO nekotorykh vyrozhdennykh ellipticheskikh uravneniyakh, voznikayushchikh v geometricheskikh zadachakhО некоторых вырожденных эллиптических уравнениях, возникающих в геометрических задачахKaputstso Dol'chettaI.Капуццо ДольчеттаИ.capuzzo@mat.uniroma1.itLeoniF.ЛеониФ.leoni@mat.uniroma1.itVitoloA.ВитолоА.vitolo@unisa.itУниверситет Сапиенца1512201558VOL 58, NO (2015)ТОМ 58, № (2015)9611020112022Copyright ©; 2022, Contemporary Mathematics. Fundamental DirectionsCopyright ©; 2022, Современная математика. Фундаментальные направления2022Contemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направленияhttps://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/CMFD/article/view/32665Мы рассматриваем некоторые вполне нелинейные вырожденные эллиптические операторы и исследуем справедливость определенных свойств, связанных с принципом максимума. В частности, мы устанавливаем эквивалентность между свойством распространения знака и строгой положительностью подходящим образом определенного обобщенного главного собственного значения. Также мы показываем, что даже в вырожденном случае, рассмотренном в настоящей работе, хорошо известное условие на член нулевого порядка, введенное Келлером-Оссерманом, является необходимым и достаточным для существования целых слабых субрешений.1.Ambrosio L., Soner H. M. Level set approach to mean curvature ow in arbitrary codimension// J. Di er. Geom. - 1996. - 43. - C. 693-737.2.Amendola M. E., Galise G., Vitolo A. 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