Partial Differential Equations and Calculus of Variations

H. D. Alber (auth.), Stefan Hildebrandt, Rolf Leis (eds.)9780387505084, 0-387-50508-3

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.

---

Table of contents :
On the existence in the large of solutions to the one-dimensional, isentropic hydrodynamic equations in a bounded domain….Pages 1-22
Initial-boundary value and scattering problems in mathematical physics….Pages 23-60
On shape optimization of a turbine blade….Pages 61-95
Free boundary problems for the Navier-Stokes equations….Pages 96-115
A geometric maximum principle, plateau’s problem for surfaces of prescribed mean curvature, and the two dimensional analogue of the catenary….Pages 116-141
Finite Elements for the Beltrami operator on arbitrary surfaces….Pages 142-155
Comparison principles in capillarity….Pages 156-197
Remarks on diagonal elliptic systems….Pages 198-210
Quasiconvexity, growth conditions and partial regularity….Pages 211-237
The monotonicity formula in geometric measure theory, and an application to a partially free boundary problem….Pages 238-255
Isoperimetric problems having continua of solutions….Pages 256-263
Harmonic maps — Analytic theory and geometric significance….Pages 264-296
Asymptotic behavior of solutions of some quasilinear elliptic systems in exterior domains….Pages 297-316
Decomposition theorems and their application to non-linear electro- and magneto-static boundary value problems….Pages 317-340
Initial boundary value problems in thermoelasticity….Pages 341-358
Applications of variational methods to problems in the geometry of surfaces….Pages 359-378
Open problems in the degree theory for disc minimal surfaces spanning a curve in ℝ 3 ….Pages 379-401
On a modified version of the free geodetic boundary-value problem….Pages 402-423