27 citations · 54 across the 13 of their papers we have counts for
4 papers · 2 filters
A remark on nonlocal Neumann conditions for the fractional Laplacian
Nicola Abatangelo
We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfy…
Getting acquainted with the fractional Laplacian
Nicola Abatangelo, Enrico Valdinoci
These are the handouts of an undergraduate minicourse at the Università di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and relat…
Positive powers of the Laplacian: from hypersingular integrals to boundary value problems
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña
Any positive power of the Laplacian is related via its Fourier symbol to a hypersingular integral with finite differences. We show how this yields a pointwise evaluation which is m…
Integral representation of solutions to higher-order fractional Dirichlet problems on balls
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña
We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power of the Laplacian. We are able to prescribe values…