Partial Differential Equations and Calculus of Variations

1. Front Matter

   Pages N2-VI

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2. On the existence in the large of solutions to the one-dimensional, isentropic hydrodynamic equations in a bounded domain

   • H. D. Alber

   Pages 1-22

3. Initial-boundary value and scattering problems in mathematical physics

   • H. D. Alber, R. Leis

   Pages 23-60

4. On shape optimization of a turbine blade

   • Hans Wilhelm Alt

   Pages 61-95

5. Free boundary problems for the Navier-Stokes equations

   • Josef Bemelmans

   Pages 96-115

6. A geometric maximum principle, plateau’s problem for surfaces of prescribed mean curvature, and the two dimensional analogue of the catenary

   • Ulrich Dierkes

   Pages 116-141

7. Finite Elements for the Beltrami operator on arbitrary surfaces

   • Gerhard Dziuk

   Pages 142-155

8. Comparison principles in capillarity

   • Robert Finn

   Pages 156-197

9. Remarks on diagonal elliptic systems

   • Jens Frehse

   Pages 198-210

10. Quasiconvexity, growth conditions and partial regularity

    • Mariano Giaquinta

    Pages 211-237

11. The monotonicity formula in geometric measure theory, and an application to a partially free boundary problem

    • Michael Grüter

    Pages 238-255

12. Isoperimetric problems having continua of solutions

    • Robert Gulliver

    Pages 256-263

13. Harmonic maps — Analytic theory and geometric significance

    • Jürgen Jost

    Pages 264-296

14. Asymptotic behavior of solutions of some quasilinear elliptic systems in exterior domains

    • Michael Meier

    Pages 297-316

15. Decomposition theorems and their application to non-linear electro- and magneto-static boundary value problems

    • A. Milani, R. Picard

    Pages 317-340

16. Initial boundary value problems in thermoelasticity

    • Reinhard Racke

    Pages 341-358

17. Applications of variational methods to problems in the geometry of surfaces

    • Michael Struwe

    Pages 359-378

18. Open problems in the degree theory for disc minimal surfaces spanning a curve in ℝ3

    • A. J. Tromba

    Pages 379-401

19. On a modified version of the free geodetic boundary-value problem

    • K. J. Witsch

    Pages 402-423

20. Back Matter

    Pages 425-427

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This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

• Boundary value problem
• Calculus of Variations
• Catenary
• Convexity
• differential equation
• maximum
• maximum principle
• measure
• minimum
• partial differential equation
• scattering theory

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