Variational and Free Boundary Problems

1. Front Matter

   Pages i-xv

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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

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.

• Blowing up
• Free Boundary Problems
• Mathematica
• Variational Problems
• behavior
• computer
• computer vision
• control
• eXist
• equation
• form
• interface
• mathematics
• operator
• stability

• 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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