Symmetrization in parabolic obstacle problems (Q1354887)

The authors prove for the solutions of a linear parabolic obstacle problem an extension of the rearrangement inequality given in the elliptic case by \textit{A. Alvino}, \textit{P. L. Lions}, and \textit{G. Trombetti} [Ann. Inst. Poincaré Anal. Non Linéaire 7, No. 2, 37-65 (1990; Zbl 0703.35007)]. The method of the proof is essentially an approximation by semidiscretization using the above recalled result concerning the elliptic case. Applications to a priori estimates or extinction in finite time are also given.