Laurence Chisholm Young

Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British 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. He moved to the US in 1949 but never sought American citizenship.

Laurence Chisholm Young
L. Ch. Young (standing right) at the ICM 1932
Born	July 14, 1905 Göttingen
Died	December 24, 2000 (aged 95) Madison, Wisconsin
Alma mater	Cambridge University
Known for	Calculus of variations, real analysis
Awards	Isaac Newton Studentship (1930) Honorary degree from Paris Dauphine University (1984)
Scientific career
Institutions	Trinity College, Cambridge University of Cape Town University of Wisconsin–Madison University of Campinas IMPA
Doctoral students	Wendell Fleming

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 also is named after him and has now been generalised in the theory of rough paths.[5]

Life and academic career

Laurence Chisholm Young was born in Göttingen,[6] the fifth of the six children of William Henry Young and Grace Chisholm Young.[7] He held positions of Professor at the University of Cape Town, South Africa, and at the University of Wisconsin-Madison. He was also a chess grandmaster.[8]

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 978-0-444-86135-1, 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.
• 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.
• 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.
• Young, L. C. (1951), "Surfaces parametriques generalisees", Bulletin de la Société Mathématique de France, 79: 59–84, doi:10.24033/bsmf.1419, MR 0046421, Zbl 0044.10203.
• Young, L. C. (1954), "A variational algorithm" (PDF), Rivista di Matematica della Università di Parma, (1), 5: 255–268, MR 0081437, Zbl 0059.09605.
• Young, L. C. (1959), "Partial area – I" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 103–113, MR 0141760, 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 0141761, 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 0141762, Zbl 0107.27402.
• Young, Laurence C. (1989), "Remarks and personal reminiscences", in Roxin, Emilio O. (ed.), 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, ISBN 9780824781682, 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. (Young 1936).
6. (Turner, Rabinowitz & Rudin 2001).
7. (Fleming & Wiegand 2004, p. 413).
8. Grace Chisholm Young at Biographies of Women Mathematicians

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, archived from the original (PDF) on 9 December 2011, retrieved 5 July 2015.

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 978-0-412-57750-5, 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.
• Roubicek, Tomas (1997), Relaxation in optimization theory and variational calculus, Berlin: De Gruyter, ISBN 978-3-11-081191-9. A thorough scrutiny of Young measures and their various generalization is in Chapter 3 from the perspective of convex compactifications.
• 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, CiteSeerX 10.1.1.120.4639, 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