The motion of elastic planar closed curves under the area-preserving condition Shinya Okabe 74H4035K5574G6574B20elastic energygradient flow with two constraintsisoperimetric inequality We consider the motion of an elastic closed curve with constant enclosed area. This motion is governed by a system involving fourth order parabolic equations. We shall prove that this system has a unique classical solution for all time and the solution converges uniformly to a stationary solution together with its derivatives of any order. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3015 10.1512/iumj.2007.56.3015 en Indiana Univ. Math. J. 56 (2007) 1871 - 1912 state-of-the-art mathematics http://iumj.org/access/