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Superlinear elliptic equation for fully nonlinear operators without growth restrictions for the data

Quaas, Alexander; Felmer, Patricio; Esteban, Maria J. (2010), Superlinear elliptic equation for fully nonlinear operators without growth restrictions for the data, Proceedings of the Edinburgh Mathematical Society, 53, 1, p. 125-141. http://dx.doi.org/10.1017/S0013091507001393

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Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-00195081
Date
2010
Journal name
Proceedings of the Edinburgh Mathematical Society
Volume
53
Number
1
Publisher
Scottish Academic Press
Pages
125-141
Publication identifier
http://dx.doi.org/10.1017/S0013091507001393
Metadata
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Author(s)
Quaas, Alexander

Felmer, Patricio

Esteban, Maria J. cc
Abstract (EN)
We deal with existence and uniqueness of the solution to the fully nonlinear equation−F(D2u)+ |u|s−1u = f(x)in Rn,where s> 1 and f satisfies only local integrability conditions. This result is well known when, instead ofthe fully nonlinear elliptic operator F, the Laplacian or a divergence-form operator is considered. Ourexistence results use the Alexandroff–Bakelman–Pucci inequality since we cannot use any variationalformulation. For radially symmetric f, and in the particular case where F is a maximal Pucci operator,we can prove our results under fewer integrability assumptions, taking advantage of an appropriatevariational formulation. We also obtain an existence result with boundary blow-up in smooth domains.
Subjects / Keywords
Pucci operator; super-linear elliptic problem; local data.; boundary explosion

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