Workshop on the Mountain Pass Theorem and its Applications

University of Surrey
Friday 25 January 2008

Organised by Tom Bridges and David Lloyd


 
The year 2008 is the 35th anniversary of the seminal paper of Ambrosetti & Rabinowitz which introduced the Mountain Pass Theorem (MPT), and it is the 15th anniversary of numerical implementation of MPT by Choi & McKenna - the Mountain Pass Algorithm (MPA). The MPT is now a major tool in nonlinear analysis and the theory of nonlinear ODEs and PDEs, and MPA is a robust algorithm for finding critical points of indefinite functionals. The recent textbook by Jabri on MPT lists over 1000 references on the subject, and scholar.google.com lists over 800 citations of the original 1973 paper. In contrast there has been relatively little activity in this area in the UK. This one-day workshop is both a celebration and an introduction to the MPT. Both fundamentals and applications will be presented. PhD students are particularly encouraged to attend.
 
This workshop is one of a series organised by the London Dynamical Systems Group, supported by the London Mathematical Society, and is organised as part of the "Themed Semester on Nonlinear PDEs" at Surrey in Spring 2008. A Winter School on Analysis of Nonlinear PDEs is also associated with the Themed Semester.
 
Speakers
 
Registration
The registration fee is £20 (participants from LDSG institutions - Imperial, Queen Mary, Surrey, UCL - are exempt from the registration fee). To register, send name, affiliation, contact information, and registration fee to Mrs Gwen Potter.
For participants who need overnight accomodation, we recommend the Guildford YMCA. It is reasonably priced and within walking distance of the university. A booking with the Guildford YMCA can be made directly via their website.
Participants travelling by car should contact us in advance to obtain a car park permit.
If you have any questions or comments please don't hesitate to contact the organisers: Tom Bridges and David Lloyd .
 

Programme

 

11.00 – 12.00

John Toland (Bath)
“Introduction to the Mountain Pass Theorem”

 

12.00 – 12.30

Luca Sbano (Warwick)
“The MPT in molecular dynamics. Part I.”

 

12.30 – 14.00

Lunch

 

14.00 – 15.00

Jiří Horák (Cologne)
“Numerical Mountain Pass Algorithm and its Applications”

 

15:00 – 15.30

Luca Sbano (Warwick)
“The MPT in molecular dynamics. Part II.”

 

15.30 – 16.00

Tea

 

16.00 – 17.00

John Toland (Bath)
“Galerkin's method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy”

 

17.00 – 18.00

Wine Reception

 

Historical and Workshop References
 
  • A. Ambrosetti & P.H. Rabinowitz. Dual variational methods in critical point theory and applications, J. Func. Anal. 14 349-381 (1973).
  • Y.S. Choi & P.J. McKenna. A mountain pass method for the numerical solution of semilinear elliptic problems, Nonlinear Analysis 20 417-437 (1993).
 
  • B. Buffoni, E. Sere & J.F. Toland. Minimization methods for quasi-linear problems with an application to periodic water waves, SIAM J. Math. Anal. 36 1080-1094 (2005).
  • B. Buffoni, E. Sere & J.F. Toland. Surface water waves as saddle points of the energy, Calc. Var. Partial Differential Equations 17 199-220 (2003).
  • D.J. Crispin & J.F. Toland. Galerkin's method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy, Calc. Var. Partial Differential Equations 23 205-226 (2005).
  • J. Horák. Constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems, Numer. Math. 98 251-276 (2004).
  • J. Horák, G.J. Lord & M.A. Peletier. Cylinder buckling: the mountain pass as an organizing center, SIAM J. Appl. Math. 66 1793-1824 (2006).
  • L. Jeanjean & J.F. Toland. Bounded Palais-Smale mountain-pass sequences, C.R. Acad. Sci. Paris Ser. I Math. 327 23-28 (1998).
  • L. Sbano & J. Southall. Periodic Solutions of the N-Body Problem with Lennard-Jones potential, University of Warwick Preprint 06/2007