Variational methods and quasilinear elliptic problems
(2011)
Files
these.pdf
Restricted Access - Adobe PDF
- 1.5 MB
Details
- Authors
- Supervisors
- Willem, Michel
- Abstract
- (en) Partial differential equations arise in many areas of modern science. They can be used as mathematical models for a lot of problems and therefore play a proeminent role in physics, finance, engineering, and other disciplines. In this thesis we consider more precisely quasilinear elliptic equations, in six different frameworks. Variational methods, inspired by variational principles of physics, are our main tool. First we prove the existence of nodal solutions of problems presenting a lack of compactness. Then we show an abstract result stating the almost everywhere convergence of gradient sequences, allowing us to obtain the existence of optimal functions for critical inequalities. Afterwards we establish that some elliptic systems modelling a mixture of Bose-Einstein condensates possess normalized solutions. Next we apply variational techniques to the prescribed mean curvature problem to find infinitely many nodal solutions. We then turn to the desingularization of ring vortices, showing how solutions of a family of free-boundary problems can be used to approximate singular solutions of the Euler equations in an ideal fluid. Finally we study removable sets for the flux of continuous vector fields.
- Affiliations
Citations
de Valeriola, S. (2011). Variational methods and quasilinear elliptic problems. https://hdl.handle.net/2078.5/46128