## Abstract We consider the Laplacian in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to a Hardy inequality for the Laplacian. As a byproduct of our method, we obtain a simple proof of a th
Hardy's Inequality for Dirichlet Forms
β Scribed by P.J. Fitzsimmons
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 110 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
We prove an abstract form of Hardy's L 2 inequality, in which the Dirichlet integral is replaced by the Dirichlet form of a general symmetric Markov process. A number of examples are provided.
π SIMILAR VOLUMES
1 . 3 ) and showed that, for a C 2 bounded domain 0, there exists a finite constant \*\*=\*\*(0) such that { J \* =1Γ4, J \* <1Γ4, \\* \*\*, \\*>\*\*. (1.4)
We extend Hardy's discrete inequality to multiple series. For an r-fold series the Ε½ . r correct constant is c , where c is the constant in Hardy's original theorem. This constant is optimum and the inequality is strict unless all variables in it are 0.