1,308 research outputs found
Gradient estimates of q-harmonic functions of fractional Schrodinger operator
We study gradient estimates of -harmonic functions of the fractional
Schr{\"o}dinger operator , in bounded
domains . For nonnegative we show that if is H{\"o}lder
continuous of order then exists for any and |\nabla u(x)| \le c u(x)/ (\dist(x,\partial D) \wedge 1). The
exponent is critical i.e. when is only H{\"o}lder
continuous may not exist. The above gradient estimates are well
known for under the assumption that belongs to the Kato
class \calJ^{\alpha - 1}. The case is different. To obtain
results for we use probabilistic methods. As a corollary, we
obtain for that a weak solution of is in fact a strong solution
A class of continua that are not attractors of any IFS
This paper presents a sufficient condition for a continuum in to be
embeddable in in such a way that its image is not an attractor of any
iterated function system. An example of a continuum in that is not an
attractor of any weakly contracting iterated function system is also given
Axial gravitational waves in FLRW cosmology and memory effects
We show initial data for gravitational axial waves, that are twice
differentiable but which are not . They generate wave pulses that
interact with matter in the radiation cosmological era. This forces the
radiation matter to rotate. This rotation is permanent - it persists after the
passage of the gravitational pulse. The observed inhomogeneities of the cosmic
microwave background radiation put a bound onto discontinuities of superhorizon
metric perturbations. We explicitly show that a class of smooth initial metrics
that are at least gives rise to gravitational wave pulses that do not
interact with the background during the radiation epoch.Comment: This version matches the published article (Phys. Rev. D 96, 063523
(2017)). A note is added on interaction of axial gravitational waves with
stars' interiors, with 3 new reference
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