TY - JOUR
T1 - Entropy penalization methods for Hamilton-Jacobi equations
AU - Gomes, Diogo A.
AU - Valdinoci, Enrico
PY - 2007/10/20
Y1 - 2007/10/20
N2 - 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.
AB - 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.
KW - Fixed points
KW - Hamilton-Jacobi equations
KW - Mather measures
KW - Semiconcave functions
UR - http://www.scopus.com/inward/record.url?scp=34447498638&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2007.04.001
DO - 10.1016/j.aim.2007.04.001
M3 - Article
AN - SCOPUS:34447498638
SN - 0001-8708
VL - 215
SP - 94
EP - 152
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 1
ER -