TY - JOUR
T1 - A NOTE ON THE MONGE–AMPÈRE TYPE EQUATIONS WITH GENERAL SOURCE TERMS
AU - QIU, Weifeng
AU - TANG, Lan
PY - 2020/11
Y1 - 2020/11
N2 - In this paper we consider numerical approximation to the generalised solutions to the Monge-Ampere type equations with general source terms. We first give some important propositions for the border of generalised solutions. Then, for both the classical and weak Dirichlet boundary conditions, we present well-posed numerical methods for the generalised solutions with general source terms. Finally, we prove that the numerical solutions converge to the generalised solution.
AB - In this paper we consider numerical approximation to the generalised solutions to the Monge-Ampere type equations with general source terms. We first give some important propositions for the border of generalised solutions. Then, for both the classical and weak Dirichlet boundary conditions, we present well-posed numerical methods for the generalised solutions with general source terms. Finally, we prove that the numerical solutions converge to the generalised solution.
KW - Convex domain
KW - Convex function
KW - Generalised solution
KW - Monge-ampére equation
KW - Oliker-prussner method
KW - Subdifferential
KW - Convex domain
KW - Convex function
KW - Generalised solution
KW - Monge-ampére equation
KW - Oliker-prussner method
KW - Subdifferential
KW - Convex domain
KW - Convex function
KW - Generalised solution
KW - Monge-ampére equation
KW - Oliker-prussner method
KW - Subdifferential
UR - http://www.scopus.com/inward/record.url?scp=85090226795&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85090226795&origin=recordpage
U2 - 10.1090/MCOM/3554
DO - 10.1090/MCOM/3554
M3 - 21_Publication in refereed journal
VL - 89
SP - 2675
EP - 2706
JO - Mathematics of Computation
JF - Mathematics of Computation
SN - 0025-5718
IS - 326
ER -