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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-00195081
Journal nameProceedings of the Edinburgh Mathematical Society
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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 / KeywordsPucci operator; super-linear elliptic problem; local data.; boundary explosion
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