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Regular analytic transformations of $ℝ^2$

100%

Gubeladze J.

Annales Polonici Mathematici

2000

tom 75

nr 2

99-109

Existence of loops for non-injective regular analytic transformations of the real plane is shown. As an application, a criterion for injectivity of a regular analytic transformation of $ℝ^2$ in terms of the Jacobian and the first and second order partial derivatives is obtained. This criterion is new even in the special case of polynomial transformations.

Inverse Function Theorems and Jacobians over Metric Spaces

75%

Granieri L.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Annales Polonici Mathematici

1 Granieri L.

1 Gubeladze J.

1 2014

1 2000

Wyniki wyszukiwania

Regular analytic transformations of $ℝ^2$

Inverse Function Theorems and Jacobians over Metric Spaces