Strongly Hyperbolic Equations and their Applications

Iwasaki, Nobuhisa

doi:10.1016/s0168-2024(08)70127-9

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H'-estimates For the Linearized Equation1

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1988

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“…However, these papers do not seem to be directly applicable since the estimates for the linearized equations are somewhat weaker than required there. We also refer to a formulation (without proof) of an implicit function theorem, based on Hormander's work, in Iwasaki's paper [9], in which only an approximate solution of the linearized equation is postulated. In the following we adapt the method developed in [15], which consists in applying alternatingly Newton's method and a smoothing process.…”

Section: H'-estimates For the Linearized Equationmentioning

confidence: 99%

A stability theorem for minimal foliations on a torus

Moser

1988

Ergod. Th. Dynam. Sys.

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Abstract. This paper is concerned with minimal foliations; these are foliations whose leaves are extremals of a prescribed variational problem, as for example foliations consisting of minimal surfaces. Such a minimal foliation is called stable if for any small perturbation of the variational problem there exists a minimal foliation conjugate under a smooth diffeomorphism to the original foliation. In this paper the stability of special foliations of codimension 1 on a higher-dimensional torus is established. This result requires small divisor assumptions similar to those encountered in dynamical systems. This theorem can be viewed as a generalization of the perturbation theory of invariant tori for Hamiltonian systems to elliptic partial differential equations for which one obtains quasi-periodic solutions.

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Section: H'-estimates For the Linearized Equationmentioning

confidence: 99%

A stability theorem for minimal foliations on a torus

Moser

1988

Ergod. Th. Dynam. Sys.

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show abstract

Strongly Hyperbolic Equations and their Applications

Cited by 1 publication

References 32 publications

A stability theorem for minimal foliations on a torus

A stability theorem for minimal foliations on a torus

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