On a Modified Conjecture of De Giorgi
✍ Scribed by Matthias Röger; Reiner Schätzle
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- French
- Weight
- 443 KB
- Volume
- 254
- Category
- Article
- ISSN
- 0025-5874
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We consider bounded entire solutions of the nonlinear PDE ∆u + 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
## 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