We establish the local and global Poincaré inequalities with the Radon measure for the solutions to the nonlinear elliptic partial differential equation for differential forms.
Fractional Poincaré inequalities for general measures
✍ Scribed by Clément Mouhot; Emmanuel Russ; Yannick Sire
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 169 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0021-7824
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📜 SIMILAR VOLUMES
We first prove local versions of the Poincare inequality for solutions to the Á-harmonic equation. Then, as applications of the local results, we obtain the global versions of the Poincare inequality for solutions to the A-harmonic equation śŽ . s in L , 0 -averaging domains and L -averaging domains
Taking lim sup L Ä lim k Ä in both sides of (2.10), by (i), (2.8), (2.9), and the fact that lim k Ä \* k =1 we get a contradiction. Hence, , is not identically zero.
## Abstract It is known that the classic Korn inequality is not valid for Hölder __α__ domains. In this paper, we prove a family of weaker inequalities for this kind of domains, replacing the standard __L^p^__‐norms by weighted norms where the weights are powers of the distance to the boundary. In