Laurence Chisholm Young

Laurence Chisholm Young
Born	July 14, 1905 Göttingen
Died	December 24, 2000 (aged 95) Madison, Wisconsin
Institutions	Trinity College, Cambridge University of Cape Town University of Wisconsin–Madison University of Campinas IMPA
Alma mater	Cambridge University
Doctoral students	Wendell Fleming
Known for	Calculus of variations, real analysis
Notable awards	Isaac Newton Studentship (1930) Honorary degree from Paris Dauphine University (1984)

Laurence Chisholm Young (14 July 1905 – 24 December 2000) was an American mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians.

The concept of Young measure is named after him: he also introduced the concept of the generalized curve^[1] and a concept of generalized surface^[2] which later evolved in the concept of varifold.^[3][4] The Young integral (Young (1936)) also is named after him and has now been generalised in the theory of rough paths.

Life and academic career

Laurence Chisholm Young was born in Göttingen,^[5] the fifth of the six children of William Henry Young and Grace Chisholm Young.^[6]

Selected publications

Books

• Young, L. C. (1927), The Theory of Integration, Cambridge Tracts in Mathematics and Mathematical Physics, 21, Cambridge: Cambridge University Press, pp. viii + 53, JFM 53.0207.19, available from the Internet archive.
• Young, L. C. (1969), Lectures on the Calculus of Variations and Optimal Control, Philadelphia–London–Toronto: W. B. Saunders, pp. xi+331, MR 0259704, Zbl 0177.37801.
• Young, Laurence (1981), Mathematicians and their times. History of mathematics and mathematics of history, North-Holland Mathematics Studies, 48 / Notas de Matemática [Mathematical Notes], 76, Amsterdam–New York: North-Holland Publishing Co., pp. x+344, ISBN 0-444-86135-1, MR 0629980, Zbl 0446.01028.

Papers

• Young, L. C. (1936), "An inequality of the Hölder type, connected with Stieltjes integration", Acta Mathematica, 67 (1): 251–282, doi:10.1007/bf02401743, JFM 62.0250.02, Zbl 0016.10404, (subscription required (help)).
• Young, L. C. (1937), "Generalized curves and the existence of an attained absolute minimum in the Calculus of Variations", Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III, XXX (7–9): 211–234, JFM 63.1064.01, Zbl 0019.21901, memoir presented by Stanisław Saks at the session of 16 December 1937 of the Warsaw Society of Sciences and Letters. The free PDF copy is made available by the RCIN –Digital Repository of the Scientifics Institutes.
• Young, L. C. (January 1942), "Generalized Surfaces in the Calculus of Variations", Annals of Mathematics, Second Series, 43 (1): 84–103, doi:10.2307/1968882, JFM 68.0227.03, JSTOR 1968882, MR 0006023, Zbl 0063.09081, (subscription required (help)).
• Young, L. C. (July 1942a), "Generalized Surfaces in the Calculus of Variations. II", Annals of Mathematics, Second Series, 43 (3): 530–544, doi:10.2307/1968809, JSTOR 1968809, MR 0006832, Zbl 0063.08362, (subscription required (help)).
• Young, L. C. (1951), "Surfaces parametriques generalisees", Bulletin de la Société Mathématique de France, 79: 59–84, MR 46421, Zbl 0044.10203.
• Young, L. C. (1954), "A variantional Algoritm" (PDF), Rivista di Matematica della Università di Parma, (1), 5: 255–268, MR 81437, Zbl 0059.09605.
• Young, L. C. (1959), "Partial area – I" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 103–113, MR 141760, Zbl 0107.27402.
• Young, L. C. (1959a), "Partial area. Part. II: Contours on hypersurfaces" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 171–182, MR 141761, Zbl 0107.27402.
• Young, L. C. (1959b), "Partial area. Part III: Symmetrization and the isoperimetric and least area problems" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 257–263, MR 141762, Zbl 0107.27402.
• Young, Laurence C. (1989), "Remarks and personal reminiscences", in Roxin, Emilio O., Modern optimal control: a conference in honor of Solomon Lefschetz and Joseph P. LaSalle, Lecture Notes in Pure and Applied Mathematics, 119, New York: Marcel Dekker, pp. 421–433, MR 1013226.

See also

• Bounded variation
• Caccioppoli set
• Measure theory
• Varifold

Notes

1. (Young 1937).
2. (Young 1951).
3. In his commemorative papers describing the research of Almgren, Brian White (1997, p.1452, footnote 1, 1998, p.682, footnote 1) writes that these are "essentially the same class of surfaces". He notes also that Young himself used the same term in a somewhat different context i.e. in (L. C. Young 1942, 1942a).
4. See also the 2015 unpublished essay of his pupil Wendell Fleming.
5. (Turner, Rabinowitz & Rudin 2001).
6. (Fleming & Wiegand 2004, p. 413).

References

Biographical and general references

• Fleming, Wendell H.; Wiegand, Sylvia M. (2004), "Laurence Chisholm Young (1905-2000)", Bulletin of the London Mathematical Society, 36 (3): 413–424, doi:10.1112/S0024609303002959, MR 2038729, Zbl 1050.01519
• Aubin, Jean–Pierre (1985), "Eloge du Professeur L. C. Young, Docteur Honoris Causa de l'Université Paris-Dauphine", Gazette des Mathématiciens (in French), No. 27: 98–112, MR 0803575, including a reply by L. C. Young himself (pages 109–112).
• Turner, Robert; Rabinowitz, Paul; Rudin, Mary Ellen (5 March 2001), On the death of Professor Emeritus Laurence Chisholm Young (PDF), Memorial Resolution of the Faculty of the University of Wisconsin Madison, Faculty Document 1554, p. 1.

Scientific references

• Màlek, Josef; Nečas, Jindřich; Rokyta, Mirko; Růžička, Michael (1996), Weak and measure-valued solutions to evolutionary PDEs, Applied Mathematics and Mathematical Computation, 13, London–Weinheim–New York–Tokyo–Melbourne–Madras: Chapman & Hall/CRC Press, pp. xii+317, ISBN 0-412-57750-X, MR 1409366, Zbl 0851.35002. One of the most complete monographs on the theory of Young measures, strongly oriented to applications in continuum mechanics of fluids.
• White, Brian (1997), "The Mathematics of F. J. Almgren Jr.", Notices of the American Mathematical Society, 44 (11): 1451–1456, ISSN 0002-9920, MR 1488574, Zbl 0908.01017.
• White, Brian (1998), "The mathematics of F. J. Almgren, Jr.", The Journal of Geometric Analysis, 8 (5): 681–702, doi:10.1007/BF02922665, ISSN 1050-6926, MR 1731057, Zbl 0955.01020. An extended version of (White 1997) with a list of Almgren's publications.

External links

• O'Connor, John J.; Robertson, Edmund F., "Laurence Chisholm Young", MacTutor History of Mathematics archive, University of St Andrews.
• Obituary on University of Wisconsin web site
• Laurence Chisholm Young at the Mathematics Genealogy Project