An example of researching boundary value problems correctness using diffeomorphism method
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2018.3.08Keywords:
Hilbert space, Riemannian manifold, diffeomorphism, Borel measure, derivation of measures, Laplacian, Dirichlet problemAbstract
The search for methods for checking correctness of boundary value problems in spaces of an infinite-dimensional argument is one of the problems of the infinite-dimensional analysis. In this paper, the author proposed a method to broaden the class of correct problems by reducing them to already previously considered "canonical type" problems. The reduction process consists of searching for a special class diffeomorphism between Riemannian manifolds, areas in Hilbert’s space among them, which allows to reduce the problem to a simpler one. Boundary value problems are considered in "L2-version". This paper provides an example of such a problem. To fulfill the example, Fréchet derivatives of the diffeomorphism and the inverse mapping are found; diffeomorphism boundedness — a condition of the theorem about a boundary value problem associated with diffeomorphism applicability — is proved.References
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