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Robert R. Jensen

December 11, 2023

Robert Ronald Jensen (born 6 April 1949) is an American mathematician, specializing in nonlinear partial differential equations with applications to physics, engineering, game theory, and finance.[1]

Jensen graduated in 1971 with B.S. in mathematics from Illinois Institute of Technology.[2] He received in 1975 his Ph.D. from Northwestern University with thesis Finite difference approximation to the free boundary of a parabolic variational inequality under the supervision of Avner Friedman.[3] Jensen was from 1975 to 1977 an assistant professor at the University of California, Los Angeles and from 1977 to 1980 a visiting assistant professor at the University of Wisconsin's Mathematics Research Center. At the University of Kentucky he was from 1977 to 1980 an assistant professor and from 1980 to 1987 an associate professor. At Loyola University Chicago he was from 1985 to 1986 a visiting associate professor and is since 1986 a full professor. At Loyola he was from 2007 to 2012 the chair of the department of mathematics and statistics.[2]

From 1982 to 1986 Jensen held a Sloan Fellowship. He was a visiting member of Berkeley's Mathematical Sciences Research Institute in 1992, 2005, and 2013.[2] He has given invited talks at universities and conferences around the world.[1] In 1998 he was an Invited Speaker at the International Congress of Mathematicians in Berlin.[4]

Selected publications edit

  • Barron, E.N; Evans, L.C; Jensen, R. (1984). "Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls". Journal of Differential Equations. 53 (2): 213–233. Bibcode:1984JDE....53..213B. doi:10.1016/0022-0396(84)90040-8.
  • Barron, Emmanuel Nicholas; Jensen, Robert (1986). "The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equations". Transactions of the American Mathematical Society. 298 (2): 635. doi:10.1090/S0002-9947-1986-0860384-4.
  • Jensen, R.; Lions, P.-L.; Souganidis, P. E. (1988). "A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations". Proceedings of the American Mathematical Society. 102 (4): 975. doi:10.1090/S0002-9939-1988-0934877-2.
  • Jensen, Robert (1988). "The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations". Archive for Rational Mechanics and Analysis. 101 (1): 1–27. Bibcode:1988ArRMA.101....1J. doi:10.1007/BF00281780. S2CID 5776251.
  • Jensen, Robert (1989). "Uniqueness Criteria for Viscosity Solutions of Fully Nonlinear Elliptic Partial Differential Equations". Indiana University Mathematics Journal. 38 (3): 629–667. doi:10.1512/iumj.1989.38.38030. JSTOR 24895404.
  • Barron, E. N.; Jensen, R. (1989). "Total risk aversion, stochastic optimal control, and differential games". Applied Mathematics & Optimization. 19: 313–327. doi:10.1007/BF01448203. S2CID 120524020.
  • Barron, E. N.; Jensen, R. (1990). "Semicontinuous Viscosity Solutions for Hamilton–Jacobi Equations with Convex Hamiltonians". Communications in Partial Differential Equations. 15 (12): 293–309. doi:10.1080/03605309908820745.
  • Barron, E. N.; Jensen, R. (1991). "Optimal control and semicontinuous viscosity solutions". Proceedings of the American Mathematical Society. 113 (2): 397. doi:10.1090/S0002-9939-1991-1076572-8.
  • Jensen, Robert (1993). "Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient". Archive for Rational Mechanics and Analysis. 123 (1): 51–74. Bibcode:1993ArRMA.123...51J. doi:10.1007/BF00386368. S2CID 92981091.
  • Bardi, Martino; Jensen, Robert (2002). "A Geometric Characterization of Viable Sets for Controlled Degenerate Diffusions". Set-Valued Analysis. 10 (2/3): 129–141. doi:10.1023/A:1016596318432. S2CID 118303784.
  • Barron, E. N.; Evans, L. C.; Jensen, R. (2008). "The infinity Laplacian, Aronsson's equation and their generalizations". Transactions of the American Mathematical Society. 360: 77–102. doi:10.1090/S0002-9947-07-04338-3.
  • Jensen, Robert R.; Goebel, Rafal; Barron, Emmanuel N. (2012). "The quasiconvex envelope through first-order partial differential equations which characterize quasiconvexity of nonsmooth functions". Discrete and Continuous Dynamical Systems - Series B. 17 (6): 1693–1706. doi:10.3934/dcdsb.2012.17.1693.

References edit

  1. ^ a b "Jensen, Robert". Department of Mathematics and Statistics, Loyola University Chicago.
  2. ^ a b c "Robert Jensen, Brief Professional Biography". Department of Mathematics and Statistics, Loyola University Chicago.
  3. ^ Robert R. Jensen at the Mathematics Genealogy Project
  4. ^ Jensen, Robert R. (1998). "Viscosity Solutions of Elliptic Partial Differential Equations". DOCUMENTA MATHEMATICA, Extra Volume ICM III. pp. 31–38.

External links edit

  • "Robert Jensen, Publications". Department of Mathematics and Statistics, Loyola University Chicago.

December 11, 2023
robert, jensen, robert, ronald, jensen, born, april, 1949, american, mathematician, specializing, nonlinear, partial, differential, equations, with, applications, physics, engineering, game, theory, finance, jensen, graduated, 1971, with, mathematics, from, il. Robert Ronald Jensen born 6 April 1949 is an American mathematician specializing in nonlinear partial differential equations with applications to physics engineering game theory and finance 1 Jensen graduated in 1971 with B S in mathematics from Illinois Institute of Technology 2 He received in 1975 his Ph D from Northwestern University with thesis Finite difference approximation to the free boundary of a parabolic variational inequality under the supervision of Avner Friedman 3 Jensen was from 1975 to 1977 an assistant professor at the University of California Los Angeles and from 1977 to 1980 a visiting assistant professor at the University of Wisconsin s Mathematics Research Center At the University of Kentucky he was from 1977 to 1980 an assistant professor and from 1980 to 1987 an associate professor At Loyola University Chicago he was from 1985 to 1986 a visiting associate professor and is since 1986 a full professor At Loyola he was from 2007 to 2012 the chair of the department of mathematics and statistics 2 From 1982 to 1986 Jensen held a Sloan Fellowship He was a visiting member of Berkeley s Mathematical Sciences Research Institute in 1992 2005 and 2013 2 He has given invited talks at universities and conferences around the world 1 In 1998 he was an Invited Speaker at the International Congress of Mathematicians in Berlin 4 Selected publications editBarron E N Evans L C Jensen R 1984 Viscosity solutions of Isaacs equations and differential games with Lipschitz controls Journal of Differential Equations 53 2 213 233 Bibcode 1984JDE 53 213B doi 10 1016 0022 0396 84 90040 8 Barron Emmanuel Nicholas Jensen Robert 1986 The Pontryagin maximum principle from dynamic programming and viscosity solutions to first order partial differential equations Transactions of the American Mathematical Society 298 2 635 doi 10 1090 S0002 9947 1986 0860384 4 Jensen R Lions P L Souganidis P E 1988 A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations Proceedings of the American Mathematical Society 102 4 975 doi 10 1090 S0002 9939 1988 0934877 2 Jensen Robert 1988 The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations Archive for Rational Mechanics and Analysis 101 1 1 27 Bibcode 1988ArRMA 101 1J doi 10 1007 BF00281780 S2CID 5776251 Jensen Robert 1989 Uniqueness Criteria for Viscosity Solutions of Fully Nonlinear Elliptic Partial Differential Equations Indiana University Mathematics Journal 38 3 629 667 doi 10 1512 iumj 1989 38 38030 JSTOR 24895404 Barron E N Jensen R 1989 Total risk aversion stochastic optimal control and differential games Applied Mathematics amp Optimization 19 313 327 doi 10 1007 BF01448203 S2CID 120524020 Barron E N Jensen R 1990 Semicontinuous Viscosity Solutions for Hamilton Jacobi Equations with Convex Hamiltonians Communications in Partial Differential Equations 15 12 293 309 doi 10 1080 03605309908820745 Barron E N Jensen R 1991 Optimal control and semicontinuous viscosity solutions Proceedings of the American Mathematical Society 113 2 397 doi 10 1090 S0002 9939 1991 1076572 8 Jensen Robert 1993 Uniqueness of Lipschitz extensions Minimizing the sup norm of the gradient Archive for Rational Mechanics and Analysis 123 1 51 74 Bibcode 1993ArRMA 123 51J doi 10 1007 BF00386368 S2CID 92981091 Bardi Martino Jensen Robert 2002 A Geometric Characterization of Viable Sets for Controlled Degenerate Diffusions Set Valued Analysis 10 2 3 129 141 doi 10 1023 A 1016596318432 S2CID 118303784 Barron E N Evans L C Jensen R 2008 The infinity Laplacian Aronsson s equation and their generalizations Transactions of the American Mathematical Society 360 77 102 doi 10 1090 S0002 9947 07 04338 3 Jensen Robert R Goebel Rafal Barron Emmanuel N 2012 The quasiconvex envelope through first order partial differential equations which characterize quasiconvexity of nonsmooth functions Discrete and Continuous Dynamical Systems Series B 17 6 1693 1706 doi 10 3934 dcdsb 2012 17 1693 References edit a b Jensen Robert Department of Mathematics and Statistics Loyola University Chicago a b c Robert Jensen Brief Professional Biography Department of Mathematics and Statistics Loyola University Chicago Robert R Jensen at the Mathematics Genealogy Project Jensen Robert R 1998 Viscosity Solutions of Elliptic Partial Differential Equations DOCUMENTA MATHEMATICA Extra Volume ICM III pp 31 38 External links edit Robert Jensen Publications Department of Mathematics and Statistics Loyola University Chicago Retrieved from https en wikipedia org w index php title Robert R Jensen amp oldid 1187435617, wikipedia, wiki, book, books, library,

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