TY - JOUR
T1 - A new minimizing-movements scheme for curves of maximal slope
AU - Stefanelli, Ulisse
PY - 2022
Y1 - 2022
N2 - Curves of maximal slope are a reference gradient-evolution notion in metric spaces and arise as variational formulation of a vast class of nonlinear diffusion equations. Existence theories for curves of maximal slope are often based on minimizing-movements schemes, most notably on the Euler scheme. We present here an alternative minimizing-movements approach, yielding more regular discretizations, serving as a-posteriori convergence estimator, and allowing for a simple convergence proof.
AB - Curves of maximal slope are a reference gradient-evolution notion in metric spaces and arise as variational formulation of a vast class of nonlinear diffusion equations. Existence theories for curves of maximal slope are often based on minimizing-movements schemes, most notably on the Euler scheme. We present here an alternative minimizing-movements approach, yielding more regular discretizations, serving as a-posteriori convergence estimator, and allowing for a simple convergence proof.
KW - Curves of maximal slope
KW - Generalized geodesic convexity
KW - Minimizing movements
KW - Nonlinear diffusion
KW - Wasser stein spaces
UR - http://www.scopus.com/inward/record.url?scp=85139875455&partnerID=8YFLogxK
U2 - 10.1051/cocv/2022028
DO - 10.1051/cocv/2022028
M3 - Article
SN - 1292-8119
VL - 28
JO - ESAIM: Control, Optimisation and Calculus of Variations
JF - ESAIM: Control, Optimisation and Calculus of Variations
M1 - 59
ER -