Sobolev regularity and an enhanced Jensen inequality
| dc.creator | Peletier, Mark A. | |
| dc.creator | Planqué, Robert | |
| dc.creator | Röger, Matthias | |
| dc.date | 2007-01-15 | |
| dc.date.accessioned | 2026-07-07T07:41:02Z | |
| dc.date.available | 2026-07-07T07:41:02Z | |
| dc.description | We derive a new criterion for a real-valued function $u$ to be in the Sobolev space $W^{1,2}(\R^n)$. This criterion consists of comparing the value of a functional $\int f(u)$ with the values of the same functional applied to convolutions of $u$ with a Dirac sequence. The difference of these values converges to zero as the convolutions approach $u$, and we prove that the rate of convergence to zero is connected to regularity: $u\in W^{1,2}$ if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization problem with constraints, where regularity of minimizers cannot be deduced from the Euler-Lagrange equation. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701412 | |
| dc.identifier | http://arxiv.org/abs/math/0701412 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121960 | |
| dc.subject | Functional Analysis | |
| dc.subject | Optimization and Control | |
| dc.subject | 46E35; 49J45; 49J40 | |
| dc.title | Sobolev regularity and an enhanced Jensen inequality | |
| dc.type | text |