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oai:docta.ucm.es:20.500.14352/575072023-08-26T09:47:16Zcom_20.500.14352_14col_20.500.14352_15

Isoperimetric-inequalities in the parabolic obstacle problems Díaz Díaz, Jesús Ildefonso Mossino, J. 517.956.2 Stefan problem rearrangement parabolic obstacle problems isoperimetric inequalities comparison by rearrangement accretive operators extinction in finite time Geometría diferencial Ecuaciones diferenciales 1204.04 Geometría Diferencial 1202.07 Ecuaciones en Diferencias In this paper, we are concerned with the parabolic obstacle problem (u(t)=partial derivative u/partial derivative t [GRAPHICS] (A is a linear second order elliptic operator in divergence form or a nonlinear "pseudo-Laplacian"). We give an isoperimetric inequality for the concentration of u - psi around its maximum. Various consequences are given. In particular, it is proved that u - psi vanishes after a finite time, under a suitable assumption on psi(t) + A-psi + c- psi - f. Other applications are also given. These results are deduced from the study of the particular case psi=0. In this case, we prove that, among all linear second order elliptic operators A, having ellipticity constant 1, all equimeasurable domains OMEGA, all equimeasurable functions f and u0, the choice giving the "most concentrated" solution around its maximum is: A = -DELTA, OMEGA is a ball OMEGA, f and u0 are radially symmetric and decreasing along thc radii of OMEGA. A crucial point in our proof is a pointwise comparison result for an auxiliary one-dimensional unilateral problem. This is carried out by showing that this new problem is well-posed in L(infinity) in the sense of the accretive operators theory. Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:57:21Z 2023-06-20T16:57:21Z 1992 journal article https://hdl.handle.net/20.500.14352/57507 0021-7824 eng restricted access application/pdf Elsevier