TY - JOUR
T1 - A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups
AU - Kraaij, Richard C.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - We extend the Barles-Perthame procedure [4] (see also [22]) of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f−λHf=h to the context of non-compact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamilton-equations written in terms of two equations in terms of operators H† and H‡ that serve as natural upper and lower bounds for the ‘true’ operator H. In the process, we establish a strong relation between non-linear pseudo-resolvents and viscosity solutions of Hamilton-Jacobi equations. As a consequence we derive a convergence result for non-linear semigroups.
AB - We extend the Barles-Perthame procedure [4] (see also [22]) of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f−λHf=h to the context of non-compact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamilton-equations written in terms of two equations in terms of operators H† and H‡ that serve as natural upper and lower bounds for the ‘true’ operator H. In the process, we establish a strong relation between non-linear pseudo-resolvents and viscosity solutions of Hamilton-Jacobi equations. As a consequence we derive a convergence result for non-linear semigroups.
KW - Barles-Perthame method
KW - Hamilton-Jacobi equation
KW - Non-linear semigroups
KW - Viscosity solutions
UR - http://www.scopus.com/inward/record.url?scp=85121367517&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2021.109346
DO - 10.1016/j.jfa.2021.109346
M3 - Article
AN - SCOPUS:85121367517
SN - 0022-1236
VL - 282
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 5
M1 - 109346
ER -