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

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plugin-2007-51.pdf (196.6Kb)
Date
2010
Link to item file
https://hal.archives-ouvertes.fr/hal-00195081
Dewey
Analyse
Sujet
Pucci operator; super-linear elliptic problem; local data.; boundary explosion
Journal issue
Proceedings of the Edinburgh Mathematical Society
Volume
53
Number
1
Publication date
2010
Article pages
125-141
Publisher
Scottish Academic Press
DOI
http://dx.doi.org/10.1017/S0013091507001393
URI
https://basepub.dauphine.fr/handle/123456789/3006
Collections
  • CEREMADE : Publications
Metadata
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Author
Quaas, Alexander
Felmer, Patricio
Esteban, Maria J.
Type
Article accepté pour publication ou publié
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.

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