Lawrence C. Evans

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Lawrence Craig Evans (born November 1, 1949 in Atlanta , Georgia ) is an American mathematician who deals with partial differential equations .

Lawrence Craig Evans

Life

Evans studied at Vanderbilt University (Bachelor's degree in 1971) and received his PhD in 1975 with Michael Crandall at the University of California, Los Angeles (Nonlinear evolution equations in an arbitrary Banach Space). Then he was until 1980 at the University of Kentucky and 1980 to 1989 at the University of Maryland . He has been a professor at the University of California, Berkeley since 1989 . In 1988 he was at the Institute for Advanced Study .

In 2004 he and Nicolai Krylov received the Leroy P. Steele Prize of the American Mathematical Society for the Evans-Krylov theory (developed simultaneously and independently of both). They proved the twofold differentiability ( Hölder continuity of the second derivatives) of the solutions of convex , completely nonlinear, uniformly elliptical partial differential equations and thus the existence of “classical solutions” (Evans-Krylov theorem).

In 1991 he generalized a result by Frédéric Hélein about the regularity of weakly harmonic mappings between manifolds, which in turn was generalized by Fabrice Béthuel .

He also worked on viscosity solutions of nonlinear partial differential equations, the Hamilton-Jacobi-Bellman equation in stochastic optimal control theory, harmonic map theory. His textbook on partial differential equations is a widely used university textbook in the United States.

In 1979 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ). In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (Quasiconvexity and partial regularity in the calculus of variations). He is a fellow of the American Mathematical Society . In 2014 he was elected to the National Academy of Sciences .

Fonts

  • Partial Differential Equations (= Graduate Studies in Mathematics , Volume 19). American Mathematical Society, Providence RI 1998, ISBN 0-8218-0772-2 (2nd edition. Ibid 2010, ISBN 978-0-8218-4974-3 ).
  • with Ronald F. Gariepy: Measure Theory and Fine Properties of Functions. CRC-Press, Boca Raton FL et al. a. 1992, ISBN 0-8493-7157-0 .
  • Weak convergence methods for nonlinear partial differential equations. (= Regional Conference Series in Mathematics. Volume 74). American Mathematical Society, Providence RI 1990, ISBN 0-8218-0724-2 .

Web links

Individual evidence

  1. ^ Evans: Classical solutions of fully nonlinear, convex, second-order elliptic equations. In: Communications on Pure and Applied Mathematics . Volume 35, No. 3, 1982, pp. 333-363, doi : 10.1002 / cpa . 3160350303 .
  2. ^ Evans: Partial regularity of stationary harmonic maps into spheres. In: Archive for Rational Mechanics and Analysis. Volume 116, No. 2, 1991, pp. 101-113, doi : 10.1007 / BF00375587 .
  3. ^ National Academy of Sciences Members and Foreign Associates Elected. ( Memento of the original from August 18, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Press release from the National Academy of Sciences (nasonline.org) dated April 29, 2014 @1@ 2Template: Webachiv / IABot / www.nasonline.org
personal data
SURNAME Evans, Lawrence C.
ALTERNATIVE NAMES Evans, Lawrence Craig (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH November 1, 1949
PLACE OF BIRTH Atlanta , Georgia