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Variational and Free Boundary Problems

  • Conference proceedings
  • © 1993

Overview

Editors:
  1. Avner Friedman

    1. Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA

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  2. Joel Spruck

    1. Department of Mathematics, Johns Hopkins University, Baltimore, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 53)

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Table of contents (13 papers)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Free Boundary Problems Arising in Industry

    • Avner Friedman
    Pages 1-10

  3. Convex Free Boundaries and the Operator Method

    • Andrew Acker
    Pages 11-27

  4. The Space SBV(Ω) and Free Discontinuity Problems

    • Luigi Ambrosio
    Pages 29-45

  5. Wiener Criterion for the Obstacle Problem Relative to Square Hörmander’s Operators

    • Marco Biroli, Ugo Gianazza
    Pages 47-62

  6. Asymptotic Behavior of Solidification Solutions of Stefan Problems

    • J. Chadam
    Pages 63-72

  7. Blow-Up and Regularization for the Hele-Shaw Problem

    • A. Fasano, M. Primicerio
    Pages 73-85

  8. A Multidomain Decomposition for the Transport Equation

    • Fabio Gastaldi
    Pages 87-109

  9. Axisymmetric MHD Equilibria from Kruskal-Kulsrud to Grad

    • Peter Lawrence, Edward Stredulinsky
    Pages 111-134

  10. A Two-Sided Game for Non Local Competitive Systems with Control on Source Terms

    • S. Lenhart, V. Protopopescu, S. Stojanovic
    Pages 135-152

  11. The Stefan Problem with Surface Tension

    • Stephan Luckhaus
    Pages 153-157

  12. The Rayleigh Instability for a Cylindrical Crystal-Melt Interface

    • G. B. McFadden, S. R. Coriell, B. T. Murray
    Pages 159-169

  13. Towards a Unified Approach for the Adaptive Solution of Evolution Phase Changes

    • R. H. Nochetto, M. Paolini, C. Verdi
    Pages 171-193

  14. Blowup and Global Existence for a Non-Equilibrium Phase Change Process

    • Hong-Ming Yin
    Pages 195-204
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About this book

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.

Editors and Affiliations

  • Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA

    Avner Friedman

  • Department of Mathematics, Johns Hopkins University, Baltimore, USA

    Joel Spruck

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