A sufficient condition for the lower semicontinuity of parametric integrals
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- by Edward Silverman PDF
- Trans. Amer. Math. Soc. 167 (1972), 465-469 Request permission
Abstract:
We use simple convex functions and standard techniques in area theory to treat Morrey’s extension of McShane’s lower semicontinuity theorem for parametric integrals. This enables us to eliminate some technical hypotheses, simplify the proof and obtain a more general result.References
- 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
- Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511, DOI 10.1007/978-3-540-69952-1
- T. Rado and P. V. Reichelderfer, Continuous transformations in analysis. With an introduction to algebraic topology, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXV, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955. MR 0079620
- Edward Silverman, A problem of least area, Pacific J. Math. 14 (1964), 309–331. MR 170996, DOI 10.2140/pjm.1964.14.309
- Edward Silverman, Simple areas, Pacific J. Math. 15 (1965), 299–303. MR 177321, DOI 10.2140/pjm.1965.15.299
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 167 (1972), 465-469
- MSC: Primary 49A50; Secondary 28A75
- DOI: https://doi.org/10.1090/S0002-9947-1972-0296785-5
- MathSciNet review: 0296785