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An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates.
- Source :
-
Communications in Contemporary Mathematics . Nov2019, Vol. 21 Issue 7, pN.PAG-N.PAG. 28p. - Publication Year :
- 2019
-
Abstract
- In this paper, we establish global Sobolev a priori estimates for L p -viscosity solutions of fully nonlinear elliptic equations as follows: F (D 2 u , D u , u , x) = f (x) in  Ω u (x) = φ (x) on  ∂ Ω by considering minimal integrability condition on the data, i.e. f ∈ L p (Ω) , φ ∈ W 2 , p (Ω) for n < p < ∞ and a regular domain Ω ⊂ ℝ n , and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting "fine" regularity estimates from a limiting operator, the Recession profile, associated to F to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when f ∈ p − BMO ⊋ L ∞ . In such a scenery, we show that solutions admit BMO type estimates for their second derivatives. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 21
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 139051728
- Full Text :
- https://doi.org/10.1142/S0219199718500530