Abstract
The well-known Nash inequality is extended to functions satisfying a weak Dirichlet condition in a subset of ℝn. Two versions of the inequality are established, with constants independent of the domain. The inequality is applied to obtain an estimate for the sup-norm of a solution to the linearized Stokes system, independent of the velocity field.
| Original language | English |
|---|---|
| Pages (from-to) | 287-294 |
| Number of pages | 8 |
| Journal | Pure and Applied Functional Analysis |
| Volume | 5 |
| Issue number | 2 |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020, Yokohama Publications. All rights reserved.
Keywords
- Nash inequality
- blow-up
- general domains
- linearized Stokes system
- weak Dirichlet condition