383 research outputs found
Local Hardy and Rellich inequalities for sums of squares of vector fields
We prove local refined versions of Hardy's and Rellich's inequalities as well
as of uncertainty principles for sums of squares of vector fields on bounded
sets of smooth manifolds under certain assumptions on the vector fields. We
also give some explicit examples, in particular, for sums of squares of vector
fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.Comment: 28 pages; substantially revised version: Hardy inequalities improved,
several versions of Rellich inequalities adde
On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group
In this note we construct an integral boundary condition for the Kohn
Laplacian in a given domain on the Heisenberg group extending to the setting of
the Heisenberg group M. Kac's "principle of not feeling the boundary". This
also amounts to finding the trace on smooth surfaces of the Newton potential
associated to the Kohn Laplacian. We also obtain similar results for higher
powers of the Kohn Laplacian.Comment: 14 page
- …