Quasilinear elliptic equations on noncompact Riemannian manifolds

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided. © 2017 Elsevier Inc.

Авторы
Barletta G.1 , Cianchi A.2 , Maz'ya V. 3, 4
Издательство
Academic Press Inc.
Номер выпуска
11
Язык
Английский
Страницы
3426-3462
Статус
Опубликовано
Том
273
Год
2017
Организации
  • 1 Dipartimento di Ingegneria Civile, dell'Energia, dell'Ambiente e dei Materiali, Università Mediterranea di Reggio Calabria, Via Graziella – Loc. Feo di Vito, Reggio Calabria, 89122, Italy
  • 2 Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, Firenze, 50137, Italy
  • 3 Department of Mathematics, Linköping University, Linköping, SE-581 83, Sweden
  • 4 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
Ключевые слова
Neumann problems; Noncompact manifolds; Quasilinear elliptic equations; Sobolev embeddings
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5139/