Exotic PDEs

Agostino Prástaro ()
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Agostino Prástaro: University of Roma La Sapienza, Department SBAI-Mathematics

A chapter in Mathematics Without Boundaries, 2014, pp 471-531 from Springer

Abstract: Abstract In the framework of the PDE’s algebraic topology, previously introduced by A. Prástaro, are considered exotic differential equations, i.e., differential equations admitting Cauchy manifolds N identifiable with exotic spheres, or such that their boundaries ∂ N are exotic spheres. For such equations are obtained local and global existence theorems and stability theorems. In particular the smooth (four-dimensional) Poincaré conjecture is proved. This allows to complete the previous Theorem 4.59 in Prástaro (Essays in Mathematics and Its Applications (Dedicated to Stephen Smale for his 80 th birthday), Springer, Heidelberg/New York/Dordrecht/London, pp. 369–419, 2012) also for the case n = 4.

Keywords: Integral (co)bordism groups in PDEs; Existence of local and global solutions in PDEs; Conservation laws; Crystallographic groups; Singular PDEs; Exotic spheres (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1124-0_16

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DOI: 10.1007/978-1-4939-1124-0_16

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