Abstract
In the paper, we give an abstract formulation of the classical Regge boundary value problem (but with a constant potential) in a Ililbert space and prove an isomorphism result for the problem. This result implies, in particular, maximal Lp-regularity for the problem. We also obtain an estimate of the solution with respect to the spectral parameter. Then, for one homogeneous abstract spectral problem, we find asymptotic behavior of its eigenvalues. A possible application of the abstract results to elliptic partial differential equations Is shown at the end of the paper.
| Original language | English |
|---|---|
| Pages (from-to) | 241-265 |
| Number of pages | 25 |
| Journal | Rivista di Matematica della Universita di Parma |
| Volume | 6 |
| Issue number | 2 |
| State | Published - 2015 |
| Externally published | Yes |
Keywords
- Differential-operator equations
- Eigenvalues
- Elliptic equations
- Isomorphism
- Maximal lp-regularity
- Regge problem
- Scattering problem
- Spectral parameter
All Science Journal Classification (ASJC) codes
- Mathematics(all)