Exact Green's formula for the fractional Laplacian and perturbations
Research output: Contribution to journal › Journal article › peer-review
Documents
- Exact Green's formula for the fractional Laplacian and perturbations
Accepted author manuscript, 284 KB, PDF document
Let Omega be an open, smooth, bounded subset of R-n. In connection with the fractional Laplacian (-Delta)(a) (a > 0), and more generally for a 2a-order classical pseudodifferential operator (psi do) P with even symbol, one can define the Dirichlet value gamma(a-1)(0) u, resp. Neumann value gamma(a-1)(1) u of u(x), as the trace, resp. normal derivative, of u/d(a-1) on partial derivative Omega, where d(x) is the distance from x is an element of Omega to partial derivative Omega; they define well-posed boundary value problems for P.
A Green's formula was shown in a preceding paper, containing a generally nonlocal term (B gamma(a-1)(0) u, gamma(a-1)(0) v)partial derivative Omega, where B is a first-order psi do on partial derivative Omega. Presently, we determine B from L in the case P = L-a, where L is a strongly elliptic second-order differential operator. A particular result is that B = 0 when L = -Lambda, and that B is multiplication by a function (is local) when L equals -Delta plus a first-order term. In cases of more general L, B can be nonlocal.
Original language | English |
---|---|
Journal | Mathematica Scandinavica |
Volume | 126 |
Issue number | 3 |
Pages (from-to) | 568-592 |
ISSN | 0025-5521 |
DOIs | |
Publication status | Published - 2020 |
- MU-TRANSMISSION
Research areas
Number of downloads are based on statistics from Google Scholar and www.ku.dk
ID: 257707144