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We prove the Kato conjecture for elliptic operators and N×N-systems in divergence form of arbitrary order 2m on
$ \Bbb R^n $
. More precisely, we assume the coefficients to be bounded measurable and the ellipticity is taken in the sense of a Gårding inequality. We identify the domain of their...
We consider an equation for the evolution of growing and dividing cells, and show, using a result of Kato and McLeod, that the probability density function for the stationary size distribution is necessarily unimodal.
We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.
Kiselev and Simon () considered rank one singular perturbations of general type and formulate such perturbation in terms of a resolvent formula. In an attempt to generalize it beyond the rank one case, it is found that this expression in its generality describes resolvents of a rather wide...
We extend Serrin's regularity class for weak solutions of the Navier-Stokes equations to a larger class replacing the Lebesgue spaces by Lorentz spaces.
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