Preprints:

  [P7]  E. R. Jakobsen and A. Rutkowski.

Towards a Schauder theory for fractional viscous Hamilton-Jacobi equations.

Preprint: https://arxiv.org/abs/2403.03884

  [P6]  E. R. Jakobsen and A. Rutkowski.

The master equation for mean field game systems with fractional and nonlocal diffusions.

Preprint: https://arxiv.org/abs/2305.18867

  [P5]  F. del Teso and E. R. Jakobsen.

A convergent finite difference-quadrature scheme for the porous medium equation with nonlocal pressure.

Preprint: https://arxiv.org/abs/2303.05168

  [P4]   I. Chowdhury, E. R. Jakobsen, and M. Krupski.

On fully nonlinear parabolic mean field games with examples of nonlocal and local diffusions.

Preprint: https://arxiv.org/abs/2104.06985

  [P3]  F. del Teso, J. Endal, and E. R. Jakobsen.

On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type.

In Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis, pp. 129-168, EMS Series of Congress Reports, 2018. Preprint: arXiv.

  [P2]  J. Droniou and E. R. Jakobsen

A uniformly converging scheme for fractal conservation laws.

In Proceedings of FVAC7 -- The International Symposium of Finite Volumes for Complex Applications VII held in Berlin, Germany, 2014, pp. 237-245, Springer Proceedings in Mathematics, 2014. Preprint: PDF.

  [P1]  K. Debrabant and E. R. Jakobsen

Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations.

In Proceedings of HYP2012 The 14th International Conference on Hyperbolic Problems held in Padova, Italy, 2012. AIMS, 2014. Preprint: PDF.

Publications in refereed journals:

  [47]  N. Alibaud, J. Endal, and E. R. Jakobsen.

Optimal stability results and nonlinear duality for L-infinity entropy and L1 viscosity solutions.

To appear in J. Math. Pures Appl. (Preprint: arxiv:1812.02058)

  [46]  I. Chowdhury and E. R. Jakobsen.

Precise Error Bounds for Numerical Approximations of Fractional HJB Equations.

To appear in IMA J. Numer. Anal. (Preprint: arxiv:2308.16434)

  [45]  F. del Teso, J. Endal, E. R. Jakobsen, and J. L. Vazquez.

Evolution Driven by the Infinity Fractional Laplacian.

Calc. Var. 62(136), 2023. (Preprint: arxiv:2210.06414)

  [44]  F. del Teso, J. Endal, and E. R. Jakobsen.

Uniform tail estimates and Lp-convergence for finite-difference approximations of nonlinear diffusion equations.

Discrete Contin. Dyn. Syst. 43(3&4): 1319-1346, 2023. (Preprint: arxiv:2202.02297)

  [43]  I. Chowdhury, O. Ersland, and E. R. Jakobsen.

On Numerical Approximations of Fractional and Nonlocal Mean Field Games.

Found. Comput. Math. 23:1381–1431, 2023. (Preprint: arxiv:2105.00073)

  [42]  O. Ersland and E. R. Jakobsen.

On fractional and nonlocal parabolic Mean Field Games in the whole space.

J. Differential Equations 301: 428-470, 2021. (Preprint: arxiv:2003.12302)

  [41]   K. Grunert, H. Holden, E. R. Jakobsen, and N. C. Stenseth.

Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig-MacArthur perdator-prey model.

Proc. Natl. Acad. Sci. USA 118 (4), 2021.

  [40]   N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen.

The Liouville theorem and linear operators satisfying the maximum principle.

J. Math. Pures Appl., 142: 229-242, 2020. (Preprint: arXiv)

  [39]   F. del Teso, J. Endal, and E. R. Jakobsen.

Robust numerical methods for local and nonlocal equations of porous medium type. Part I: Theory.

SIAM J. Numer. Anal. 57(5): 2266-2299, 2019. (Preprint: arXiv)

  [38]  E. R. Jakobsen, A. Picarelli, C. Reisinger

Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems.

Electon. Commun. Probab. 24(59):1-10, 2019. (Preprint: arXiv)

  [37]   I. H. Biswas, I. Chowdhury, and E. R. Jakobsen.

On the rate of convergence for monotone numerical schemes for nonlocal Isaacs equations.

SIAM J. Numer. Anal. 57(2): 799-827, 2019. (Preprint: arXiv)

  [36]   F. del Teso, J. Endal, and E. R. Jakobsen.

Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments.

SIAM J. Numer. Anal. 56(6): 3611-3647, 2018. (Preprint: arXiv)

  [35]   L. Chen and E. R. Jakobsen.

L1 semigroup generation for Fokker-Planck operators associated with general Levy driven SDEs.

Discrete Contin. Dyn. Syst. 38(11): 5735-5763, 2018. (Preprint: arXiv)

  [34]   L. Chen, E. R. Jakobsen, and A. Naess

On numerical density approximations of solutions of SDEs with unbounded coefficients.

Adv. Comput. Math., 44(3): 693-721, 2018 (Preprint: arXiv)

  [33]   F. del Teso, J. Endal, and E. R. Jakobsen.

On distributional solutions of local and nonlocal problems of porous medium type.

C. R. Math. Acad. Sci. Paris 355(11): 1154-1160, 2017. (Preprint: arXiv)

  [32]   E. Chasseigne and E. R. Jakobsen

On nonlocal quasilinear equations and their local limits.

J. Differential Equations 262(6): 3759-3804, 2017. (Preprint: arXiv)

  [31]  F. del Teso, J. Endal, and E. R. Jakobsen

Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type.

Advances in Mathematics 305: 78-143, 2017. (Preprint: arXiv)

  [30]   J. Endal and E. R. Jakobsen

L1 contraction for bounded (non-integrable) solutions of degenerate parabolic equations.

SIAM J. Math. Anal. 46(6): 3957-3982, 2014. (Preprint: PDF)

  [29]   N. Alibaud, S. Cifani, and E. R. Jakobsen.

Optimal continuous dependence estimates for fractional degenerate parabolic equations.
Arch. Ration. Mech. Anal. 213(3): 705-762, 2014. (Preprint: PDF)

  [28]   G. Barles, E. Chasseigne, C. Georgelin, and E. R. Jakobsen.

On Neumann type problems for non-local equations set in a half space.
Trans. Amer. Math. Soc. 366(9): 4873-4917, 2014. (Preprint: PDF)

  [27]   S. Cifani and E. R. Jakobsen.

On numerical methods and error estimates for degenerate fractional convection-diffusion equations.
Numer. Math. 127(3): 447-483, 2014. (Preprint: PDF).

  [26]   G. Barles, C. Georgelin, and E. R. Jakobsen.

On Neumann and oblique derivatives boundary conditions for nonlocal elliptic equations.
J. Differential Equations. 256(4): 1368-1394, 2014. (Preprint: PDF).

  [25]   S. Cifani and E. R. Jakobsen.

On the spectral vanishing viscosity method for periodic fractional conservation laws.
Math. Comp. 82: 1489-1514, 2013. (Preprint: PDF)

  [24]   K. Debrabant and E. R. Jakobsen.

Semi-Lagrangian schemes for linear and fully non-linear diffusion equations.
Math. Comp. 82: 1433-1462, 2013. (Preprint: PDF)

  [23]   N. Alibaud, S. Cifani, and E. R. Jakobsen.

Continuous dependence estimates for nonlinear fractional convection-diffusion equations.
SIAM J. Math. Anal. 44(2): 603-632, 2012. (Preprint: PDF)

  [22]   S. Cifani, E. R. Jakobsen, and K. H. Karlsen.

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations.
BIT 51(4): 809-844, 2011. (Preprint: PDF )

  [21]   S. Cifani, E. R. Jakobsen, and K. H. Karlsen.

The discontinuous Galerkin method for fractal conservation laws.
IMA J. Numer. Anal. 31(3): 1090-1122, 2011. (Preprint: PDF)

  [20]   S. Cifani and E. R. Jakobsen.

Entropy solution theory for fractional degenerate convection-diffusion equations.
Ann. Inst. H. Poincare Anal. Non Lineaire 28(3): 413-441, 2011. (Preprint: PDF)

  [19]   I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen.

Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE.
SIAM J. Numer. Anal. 48(3): 1110-1135, 2010. (Preprint: PDF)

  [18]   I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen.

Viscosity solutions for a system of integro-PDEs and connections to optimal switching and control of jump-diffusion processes.
Appl. Math. Optim. 62(1): 47-80, 2010. (Preprint: PDF)

  [17]   F. Camilli and E. R. Jakobsen.

A Finite Element like Scheme for Integro-Partial Differential Hamilton-Jacobi-Bellman Equations.
SIAM J. Numer. Anal. 47(4): 2407-2431, 2009. (Preprint: PDF)

  [16]  E. R. Jakobsen, K. H. Karlsen, and C. La Chioma.

Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions.
Numer. Math. 110(2): 221-255, 2008. (Preprint: PDF)

  [15]  E. R. Jakobsen and C. A. Georgelin.

Continuous dependence results for non-linear Neumann type boundary value problems.
J. Differential Equations 245(9): 2355-2704, 2008. (Preprint: PDF)

  [14]   I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen.

Error estimates for a class of finite difference-quadrature schemes for fully nonlinear degenerate parabolic integro-PDEs.
J. Hyperbolic Differ. Equ. 5(1): 187-219, 2008. (Preprint: PDF)

  [13]  G. Barles and E. R. Jakobsen.

Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations.
Math. Comp. 76(240): 1861-1893, 2007. (Preprint: PDF)

  [12]  E. R. Jakobsen.

On error bounds for monotone approximation schemes for multi-dimensional Isaacs equations.
Asymptotic Analysis 49(3,4): 249-273, 2006. (Preprint: PDF)

  [11]  E. R. Jakobsen and K. H. Karlsen.

A "maximum principle for semicontinuous functions" applicable to integro-partial differential equations.
NoDEA Nonlinear Differential Equations Appl. 13:137-165, 2006. (Preprint: PDF)

  [10]  G. Barles and E. R. Jakobsen.

Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations.
SIAM J. Numer. Anal. 43(2):540-558, 2005. (Preprint: PDF)

  [9]    E. R. Jakobsen and K. H. Karlsen.

Convergence rates for semi-discrete splitting approximations for degenerate parabolic equations with source terms.
BIT 45(1): 37-67, 2005. (Preprint: PDF)

  [8]    E. R. Jakobsen and K. H. Karlsen.

Continuous dependence estimates for viscosity solutions of integro-PDEs.
J. Differential Equations 212(2): 278-318, 2005. (Preprint: PDF)

  [7]  E. R. Jakobsen.

On error bounds for approximation schemes for non-convex degenerate elliptic equations.
BIT 44(2): 269-285, 2004. (Preprint: PDF)

  [6]  E. R. Jakobsen.

W^{2,\infty} regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension.
Proc. Amer. Math. Soc. 132(11): 3203-3213, 2004. (Article: PDF)

  [5]  E. R. Jakobsen.

On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems.
Math. Models Methods Appl. Sci. (M3AS) 13(5): 613-644, 2003. (Preprint: PDF)

  [4]  G. Barles and E. R. Jakobsen.

On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations.
M2AN Math. Model. Numer. Anal. 36(1): 33-54, 2002. (Article: PDF)

  [3]  E. R. Jakobsen and K. H. Karlsen.

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations.
Electron. J. Diff. Eqns. 2002(39): 1-10, 2002. (Article: PDF)

  [2]  E. R. Jakobsen and K. H. Karlsen.

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations.
J. Differential Equations 183: 497-525, 2002. (Article: PDF)

  [1]  E. R. Jakobsen, K. H. Karlsen, and N. H. Risebro.

On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms.
Siam J. Numer. Anal. 39(2): 499-518, 2001. (Article: PDF)

Publications in refereed conference proceedings:

  [5]   F. del Teso, J. Endal, and E. R. Jakobsen.

On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type.

In Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis, pp. 129-168, EMS Series of Congress Reports, 2018. Preprint: arXiv

  [4]   J. Droniou and E. R. Jakobsen

A uniformly converging scheme for fractal conservation laws.

In Proceedings of FVAC7 -- The International Symposium of Finite Volumes for Complex Applications VII held in Berlin, Germany, 2014, pp. 237-245, Springer Proceedings in Mathematics, 2014. Preprint: PDF.

  [3]   K. Debrabant and E. R. Jakobsen

Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations.

In Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of HYP2012 -- The 14th International Conference on Hyperbolic Problems held in Padova, Italy, 2012

AIMS conference proceedings, 2014. Preprint: PDF.

  [2]   I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen.

Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion.
In Stochastic Analysis and Partial Differential Equations, Contemp. Math. 429, pp. 19--31,

Amer. Math. Soc., 2007. (Preprint: PDF)

  [1]  E. R. Jakobsen, K. H. Karlsen, and N. H. Risebro.

On the convergence rate of operator splitting for weakly coupled systems of Hamilton-Jacobi equations.

In Hyperbolic problems: theory, numerics, applications, Proceedings of HYP2000 The 8th International Conference on Hyperbolic Problems held in Magdeburg, Germany, 2000.

Internat. Ser. Numer. Math. 141, pp. 553-562, Birkhäuser, 2001. (Preprint: PDF)

Refereed chapters in books

  [2]   K. Debrabant and E. R. Jakobsen

Semi-Lagrangian schemes for parabolic equations.

In Recent Developments in Computational Finance, pp. 279--298,

World Scientific/Imperial College Press, 2013.

  [1]   E. R. Jakobsen

Monotone schemes.

In Encyclopedia of Quantitative Finance, pp. 1253-1263,

John Wiley & Sons Ltd., 2010.

Theses:

  [2]  E. R. Jakobsen.

On the Theory and Numerical Analysis of Viscosity Solutions.
Doktor Ingeniør Thesis 2001:95, Norwegian University of Science and Technology, 2001.
    Download thesis: PS, PDF.

  [1]  E. R. Jakobsen.

The Stochastic Wave Equation.
Diploma Thesis, Norwegian University of Science and Technology, 1996.
    Download thesis: PS, PDF.