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Error Estimates for the Approximation of the Effective Hamiltonian

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Abstract

We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting.

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Authors and Affiliations

  1. Dip. di Matematica Pura e Applicata, Univ. dell’Aquila, Loc. Monteluco di Roio, 67040, l’Aquila, Italy

    Fabio Camilli

  2. Dip. di Matematica, Univ. di Roma “La Sapienza”, P.le Aldo Moro 2, 00185, Roma, Italy

    Italo Capuzzo Dolcetta

  3. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Diogo A. Gomes

Authors
  1. Fabio Camilli
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  2. Italo Capuzzo Dolcetta
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  3. Diogo A. Gomes
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Corresponding author

Correspondence to Fabio Camilli.

Additional information

D.G. was partially supported by the Center for Mathematical Analysis, Geometry and Dynamical Systems through FCT Program POCTI/FEDER and by grant POCI/FEDER/MAT/55745/2004.

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Camilli, F., Capuzzo Dolcetta, I. & Gomes, D.A. Error Estimates for the Approximation of the Effective Hamiltonian. Appl Math Optim 57, 30–57 (2008). https://doi.org/10.1007/s00245-007-9006-9

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