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math.AP2012★ 1 cited
An obstacle problem for a class of Monge-Ampère type functionals
Jiakun Liu, Bin Zhou
In this paper we study an obstacle problem for Monge-Ampère type functionals, whose Euler-Lagrange equations are a class of fourth order equations, including the affine maximal sur…
math.AP2012
Light reflection is nonlinear optimization
Jiakun Liu
In this paper, we show that the near field reflector problem is a nonlinear optimization problem. From the corresponding functional and constraint function, we derive the Monge-Amp…