Entropy penalization methods for Hamilton-Jacobi equations

• Autores: Diogo A. Gomes, Enrico Valdinoci
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 215, Nº 1, 2007, págs. 94-152
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.04.001
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• Resumen

  • In this paper we present a new entropy penalization problem and we discuss its relations with approximate solutions of Hamilton-Jacobi equations, the convergence of associated discrete schemes, as well as several applications, such as: a generalization of the Hopf-Cole transformation which converts non-linear Hamilton-Jacobi equations into linear evolution equations, the study of fixed point problems, approximation of certain linear evolution equations, and the construction of entropy penalized Mather measures.