1,721,378 research outputs found
Observations and diagnostics in high brightness beams
Full text linkBrightness is a figure of merit largely used in light sources, such as free-electron lasers, but it is also fundamental in several other applications, forinstance, Compton back-scattering sources, beam-driven plasma acceleratorsand terahertz sources. Advanced diagnostics is mandatory for the developmentof high brightness beams. 6D electron-beam diagnostics will be reviewed, withemphasis on emittance measurement
Best remainder norms in Sobolev-Hardy inequalities
No full textWe exhibit the optimal norm for a remainder term in
the sharp Sobolev inequality involving a Lorentz norm, and in the
equivalent classical Hardy inequality. Limiting cases of the
relevant inequalities are also considered
Improving sharp Sobolev type inequalities by optimal remainder gradient norms
No full textWe are concerned with Sobolev type inequalities in
, \Omega \subset \rn, with optimal target
norms and sharp constants. Admissible remainder terms depending on
the gradient are characterized. As a consequence, the strongest
possible remainder norm of the gradient is exhibited. Both the
case when and the borderline case when are
considered. Related Hardy inequalities with remainders are also
derived
Hardy inequalities with non-standard remainder terms
No full textStarting point in this paper is the classical Hardy inequality with optimal constant and the lackness of extremals for funtions in the Sobolev space W^{1,p}(R^n). The lack of extremal has inspired improved versions, where the whole space R^n is replaced by any open bounded subset containing the origin and that amount to extra terms on the left-hand side that either involve integrals of |u|^p with weights depending on |x| which are less singular than |x|^{-p} at zero or integrals of |Du|^q with q<p. In this paper it is estabilished a stregthened version in the whole of R^n with a remainder term having a different nature. Such a remainder depends on a distance of u, in a suitable norm, from the family of those functions that can be regarded as the virtual extremals in the Hardy inequality
Dirichlet integrals and Steiner asymmetry
No full textAbstractThe asymmetry of a Sobolev function u, measured as an integral distance from its Steiner symmetral us, is estimated in terms of the gap between the Dirichlet integrals of u and us
Steiner symmetric extremals in Polya-Szego type inequalities
No full textThe cases of equality are analyzed in Steiner symmetrization inequalities for Dirichlet-type integrals. In particular, minimal assumptions are determined under which functions attaining equality are necessarily Steiner symmetric
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