Some inequalities for the Poincaré metric of plane domains
✍ Scribed by Toshiyuki Sugawa; Matti Vuorinen
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- French
- Weight
- 247 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0025-5874
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let D be a bounded strictly convex domain in Euclidean n-space equipped with its Hilbert metric h(x; y). It is shown that as the points x and y of D approach distinct points on the boundary of D, for any a in D the sum h(x; a) + h(a; y) is asymptotic to h(x; y).
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