arXiv subjects

Ralph Chill

Publications and source records attributed to Ralph Chill.

22 records · Page 2Linked to original sources

arXiv2015

Quantified versions of Ingham's theorem

We obtain quantified versions of Ingham's classical Tauberian theorem and some of its variants by means of a natural modification of Ingham's own simple proof. As corollaries of the main general results, we obtain quantified decay estimates for $C_0$-semigroups. The results reproduce those known in the literature but are both more general and, in one case, sharper. They also lead to a better understanding of the previously obscure "fudge factor' appearing in proofs based on estimating contour integrals.

math.FA↗

arXiv2014

Application of the $j$-subgradient in a problem of electropermeabilisation

We study a coupled elliptic-parabolic Poincaré-Steklov system arising in electrical cell activity in biological tissues. By using the notion of $j$-subgradient, we show that this system has a gradient structure and thus obtain wellposedness. We further exploit the gradient structure for the discretisation of the problem and provide numerical experiments.

math.AP↗

arXiv2014

Weighted inequalities for singular integral operators on the half-line

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of the operators satisfy relaxed Dini conditions. We apply the weighted estimates to extrapolation of maximal $L^p$ regularity of first order, second order and fractional order Cauchy problems into weighted rearrangement invariant Banach function spaces. In particular, we provide extensions, as well as a unification of recent results due to Auscher and Axelsson, and Chill and Fiorenza.

math.CA↗

arXiv2014

Maximal regularity in interpolation spaces for second order Cauchy problems

We study maximal regularity in interpolation spaces for the sum of three closed linear operators on a Banach space, and we apply the abstract results to obtain Besov and Hölder maximal regularity for complete second order Cauchy problems under natural parabolicity assumptions. We discuss applications to partial differential equations.

math.FA↗