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Conformal invariants measuring the best constants for Gagliardo-Nirenberg-Sobolev inequalities
We introduce a family of conformal invariants associated to a smooth metric
measure space which generalize the relationship between the Yamabe constant and
the best constant for the Sobolev inequality to the best constants for
Gagliardo-Nirenberg-Sobolev inequalities . These invariants are constructed via a minimization
procedure for the weighted scalar curvature functional in the conformal class
of a smooth metric measure space. We then describe critical points which are
also critical points for variations in the metric or the measure. When the
measure is assumed to take a special form --- for example, as the volume
element of an Einstein metric --- we use this description to show that
minimizers of our invariants are only critical for certain values of and
. In particular, on Euclidean space our result states that either
or , giving a new characterization of the GNS inequalities whose
sharp constants were computed by Del Pino and Dolbeault.Comment: 20 page
Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian
We establish a family of sharp Sobolev trace inequalities involving the
-norm. These inequalities are closely related
to the realization of fractional powers of the Laplacian on
as generalized Dirichlet-to-Neumann
operators associated to powers of the weighted Laplacian in upper half space,
generalizing observations of Caffarelli--Silvestre and of Yang.Comment: 25 page
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Delivering knowledge in the field: A telecommunications service provision and maintenance case
This paper proposes a novel approach to providing knowledge management services in a business
process wherein field engineers are the main process actors, providing and maintaining
telecommunications services. Cooperating multi-agents play a central role for the provision of
knowledge management services by integrating heterogeneous systems to collect related knowledge
for the execution of mobile tasks. The proposed system is expected to increase both the performance of
the mobile workforce and customer satisfaction by supporting and encouraging knowledge sharing
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