On the existence of functions having given partial derivatives on a curve

Author:
Maurice Sion

Journal:
Trans. Amer. Math. Soc. **77** (1954), 179-201

MSC:
Primary 27.2X

MathSciNet review:
0064846

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References | Similar Articles | Additional Information

**[1]**Anthony P. Morse,*The behavior of a function on its critical set*, Ann. of Math. (2)**40**(1939), no. 1, 62–70. MR**1503449**, 10.2307/1968544**[2]**Arthur Sard,*The measure of the critical values of differentiable maps*, Bull. Amer. Math. Soc.**48**(1942), 883–890. MR**0007523**, 10.1090/S0002-9904-1942-07811-6**[3]**Hassler Whitney,*Analytic extensions of differentiable functions defined in closed sets*, Trans. Amer. Math. Soc.**36**(1934), no. 1, 63–89. MR**1501735**, 10.1090/S0002-9947-1934-1501735-3**[4]**Hassler Whitney,*A function not constant on a connected set of critical points*, Duke Math. J.**1**(1935), no. 4, 514–517. MR**1545896**, 10.1215/S0012-7094-35-00138-7**[5]**W. M. Whyburn,*Non-isolated critical points of functions*, Bull. Amer. Math. Soc.**35**(1929), no. 5, 701–708. MR**1561794**, 10.1090/S0002-9904-1929-04806-7

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DOI:
https://doi.org/10.1090/S0002-9947-1954-0064846-0

Article copyright:
© Copyright 1954
American Mathematical Society