Publications - Adam Oberman Math

Publications

Accepted/To Appear

  1. (with Jean-David Benamou and Brittany Froese) Two Numerical Methods for the Elliptic Monge-Ampere Equation,
  2. Convergence Rates for Difference Schemes for Polyhedral Nonlinear Parabolic Equations, . J. Comput. Math.
  3. (with Luis Silvestre) The Dirichlet Problem for the Convex Envelope, Trans. Amer. Math. Soc.

Published

  1. (with Brittany Froese) Numerical Averaging of Non-Divergence Structure Elliptic Operators, Comm. Math. Sci, Vol. 7 (2009), No. 4, pp 785-804
  2. (with Ryo Takei and Alexander Vladimirsky) Homogenization of Metric Hamilton-Jacobi Equations, SIAM Multiscale Modeling and Simulation, Vol. 8 Number 1 (2009) 269-295
  3. (with Diogo Gomes) Viscosity Solutions Methods for Converse KAM Theory, ESAIM: M2AN, Vol. 42 (2008) 1047-1064.
  4. Computing the convex envelope using a nonlinear partial differential equation, Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 18. No 5 (2008) 759-780
  5. Wide stencil finite difference schemes for the elliptic Monge-Ampere equation and functions of the eigenvalues of the Hessian, Discrete and Continuous Dynamical Systems series B (DCDS B) Volume 10, Number 1, July 2008 (221-238)
  6. An explicit solution of the Lipschitz extension problem, Proc. Amer. Math. Soc. 136 (2008) 4329-4338.
  7. The convex envelope is the solution of a nonlinear obstacle problem, Proc. Amer. Math. Soc. 135 (2007), no. 6, 1689--1694
  8. Convergent Difference Schemes for Nonlinear Elliptic and Parabolic Equations: Hamilton-Jacobi Equations and Free Boundary Problems, SIAM Journal on Numerical Analysis, Vol 44 (2006) No. 2 pp. 879-895.
  9. A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions, Mathematics of Computation, 74 (2005) Number 251, 1217-1230.
  10. A convergent monotone difference scheme for motion of level sets by mean curvature, Numerische Mathematik, Volume 99 (2004) Number 2 pages 365-379.
  11. (with Robert McCann) Exact semigeostrophic flows in an elliptical basin, Nonlinearity, Volume 17 pages 1891-1922 (2004).
  12. (with Diogo Gomes) Computing the effective Hamiltonian using a variational approach, SIAM Journal on Control and Optimization, Volume 43 (2004) Number 3 pages 793-812.
    • journal link
    • ObermanGomes.pdf
    • Later appeared in: Proceedings of the Joint 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05), Seville, Spain, December 12-15 (2005).
  13. (with T. Zariphopoulou) Pricing early exercise contracts in incomplete markets, Computational Management Science, Vol 1 Issue 1 December (2003) pages 75-107.
  14. (with P. Constantin, A. Kiselev, and L. Ryzhik) Bulk burning rate in passive-reactive diffusion, Archive for Rational Mechanics, 154 (2000), 53-91.

Coauthors

Contact information and web pages of coauthors can be found at People.

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