Título: | Isoperimetric inequalities in the parabolic obstacle problems |
Autores: | Díaz Díaz, Jesús Ildefonso ; Mossino, J. |
Tipo de documento: | texto impreso |
Editorial: | Elsevier, 1992 |
Dimensiones: | application/pdf |
Nota general: | info:eu-repo/semantics/restrictedAccess |
Idiomas: | |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría diferencial , Tipo = Artículo |
Resumen: |
We are concerned with the parabolic obstacle problem ut+Au+cu?f,u??, (ut+Au+cu?f)(u??)=0inQ=(0,T)×?, u=? on ?=(0,T)×??, u|t=0=u0 in ?, A being a linear elliptic second-order operator in divergence form or a nonlinear `pseudo-Laplacian'. We give an isoperimetric inequality for the concentration of u?? around its maximum. Various consequences are given. In particular, it is proved that u?? vanishes after a finite time, under a suitable assumption on ?t+A?+c??f. Other applications are also given. "These results are deduced from the study of the particular case ?=0. In this case, we prove that, among all linear second-order elliptic operators A having ellipticity constant 1, all equimeasurable domains ?, all equimeasurable functions f and u0, the choice giving the `most concentrated' solution around its maximum is: A=??, ? is a ball ?˜, f and u0 are radially symmetric and decreasing along the radii of ?˜. "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? in the sense of the theory of accretive operators. |
En línea: | https://eprints.ucm.es/id/eprint/16387/1/125.pdf |
Ejemplares
Estado |
---|
ningún ejemplar |