Evolution problems in geometry and mathematical physiscs. (English) Zbl 0932.35045
Rossi, Hugo (ed.), Prospects in mathematics. Invited talks on the occasion of the 250th anniversary of Princeton University. Papers from the conference, Princeton, NJ, USA, March 17–21, 1996. Providence, RI: American Mathematical Society. 83-101 (1999).
Discussing the basic problems of existence and uniqueness of classical solutions, of the existence and the regularity of weak solutions in the natural energy spaces, a special emphasis is given to the common features underlying all the above mentioned equations. In particular, it is shown that there is an universal pattern of subcritical and supercritical behaviour (depending on the strength of the nonlinearity and on the space dimension) and a critical behaviour, characterized by the conformal invariance of the energy.
For the entire collection see [Zbl 0902.00027].
For the entire collection see [Zbl 0902.00027].
Reviewer: L.Ambrosio (Pisa)
MSC:
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
