Rigidity for the hyperbolic Monge-Ampère equation

研究成果: 雜誌貢獻文章同行評審

摘要

Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set K is contained in the hyperboloid H−1, where H−1 ⊂ M2 sym ×2, the set of symmetric 2 × 2 matrices. The hyperboloid H−1 is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation det ∇2u = −1. For some compact subsets K ⊂ H−1 containing a rank-one connection, we show the rigidity property of K by imposing proper topology in the convergence of approximate solutions and affine boundary conditions.

原文英語
頁(從 - 到)609-623
頁數15
期刊Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
3
發行號3
出版狀態已發佈 - 2004 一月 1
對外發佈Yes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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