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Existence of equations describing the classes of nondegenerate curvilinear coordinates in arbitrary domains. (Russian, English) Zbl 1173.35417

Zh. Vychisl. Mat. Mat. Fiz. 42, No. 1, 47-52 (2002); translation in Comput. Math. Math. Phys. 42, No. 1, 43-48 (2002).
Curvilinear coordinates in the simple connectedness domain are constructed by virtue of mapping of the unit square onto this domain. There is formulated a concept, which enables to identify classes of bijective mappings. A functional is derived, which depends upon derivative of desired functions and upon variable coefficients. These coefficients are elements of certain symmetric and positive definite matrix. There is formulated a discrete analog of variational concept.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
58E30 Variational principles in infinite-dimensional spaces
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