Variational and Free Boundary Proble - FRIEDMAN AVNER

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Résumé :
This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on Phase Transitions and Free Boundaries. The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un? known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat? isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera? ture within the water. Some free boundary problems lend themselves to variational formulation.

Sommaire:
Free boundary problems arising in industry.- Convex free boundaries and the operator method.- The space SBV(?) and free discontinuity problems.- Wiener criterion for the obstacle problem relative to square HÖrmander's operators.- Asymptotic behavior of solidification solutions of Stefan problems.- Blow-up and regularization for the Hele-Shaw problem.- A multidomain decomposition for the transport equation.- Axisymmetric MHD equilibria from Kruskal-Kulsrud to Grad.- A two-sided game for non local competitive systems with control on source terms.- The Stefan problem with surface tension.- The Rayleigh instability for a cylindrical crystal-melt interface.- Towards a unified approach for the adaptive solution of evolution phase changes.- Blowup and global existence for a non-equilibrium phase change process.