On the semi-continuity of double integrals
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- by Paul V. Reichelderfer PDF
- Trans. Amer. Math. Soc. 67 (1949), 275-285 Request permission
References
- Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946. MR 0017881
- L. Cesari, Rappresentazione quasi conforme delle superficie continue, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 1 (1946), 509–514 (Italian). MR 18218
- Lamberto Cesari, Parametrizzazione delle superficie continue di area finita secondo Lebesgue, Ann. Mat. Pura Appl. (4) 26 (1947), 301–374 (Italian). MR 27839, DOI 10.1007/BF02415383
- Lamberto Cesari, La nozione di integrale sopra una superficie in forma parametrica, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2) 13 (1944), 77–117 (1948) (Italian). MR 24510
- Philip Franklin and Norbert Wiener, Analytic approximations to topological transformations, Trans. Amer. Math. Soc. 28 (1926), no. 4, 762–785. MR 1501373, DOI 10.1090/S0002-9947-1926-1501373-8
- E. J. McShane, On the semi-continuity of double integrals in the calculus of variations, Ann. of Math. (2) 33 (1932), no. 3, 460–484. MR 1503070, DOI 10.2307/1968529
- E. J. McShane, Integrals over surfaces in parametric form, Ann. of Math. (2) 34 (1933), no. 4, 815–838. MR 1503135, DOI 10.2307/1968701
- Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957. MR 0082536
- Tibor Radó, On a lemma of McShane, Ann. of Math. (2) 42 (1941), 73–83. MR 3433, DOI 10.2307/1968988
- Tibor Radó, On the semi-continuity of double integrals in parametric form, Trans. Amer. Math. Soc. 51 (1942), 336–361. MR 5905, DOI 10.1090/S0002-9947-1942-0005905-X —Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948.
- Tibor Radó, Convergence in area, Duke Math. J. 16 (1949), 61–71. MR 28388
- Paul V. Reichelderfer, Law of transformation for essential generalized Jacobians, Duke Math. J. 16 (1949), 73–83. MR 30592
- William Scott, A note on the lower semi-continuity of double integrals in the parametric form, Bull. Amer. Math. Soc. 48 (1942), 763–767. MR 7530, DOI 10.1090/S0002-9904-1942-07778-0
- J. W. T. Youngs, On surfaces of class $K_1$, Bull. Amer. Math. Soc. 51 (1945), 669–673. MR 14420, DOI 10.1090/S0002-9904-1945-08414-6
Additional Information
- © Copyright 1949 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 67 (1949), 275-285
- MSC: Primary 27.2X
- DOI: https://doi.org/10.1090/S0002-9947-1949-0034447-7
- MathSciNet review: 0034447