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A Liouville theorem for the Neumann problem of Monge-Ampère equations.
- Source :
-
Journal of Functional Analysis . Mar2023, Vol. 284 Issue 6, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- In this paper, we study the Neumann problem of Monge-Ampère equations in Semi-space. For two dimensional case, we prove that its viscosity convex solutions must be a quadratic polynomial. When the space dimension n ≥ 3 , we show that the conclusion still holds if either the boundary value is zero or the viscosity convex solutions restricted on some n − 2 dimensional subspace is bounded from above by a quadratic function. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 284
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 161345707
- Full Text :
- https://doi.org/10.1016/j.jfa.2022.109817