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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. 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. 2023-06-20T16:57:21Z 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 Elsevier