On a conjecture of De Giorgi and some related problems
β Scribed by N. Ghoussoub; C. Gui
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 142 KB
- Volume
- 311
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free boundary. As an application we give a full positive answer to a conjecture
We consider bounded entire solutions of the nonlinear PDE βu + uu 3 = 0 in R d and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes. The proof uses a Liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form opera