30 citations · 75 across the 19 of their papers we have counts for
24 papers
A unified view of nonlinear, nonlocal operators and qualitative properties of associated elliptic and parabolic problems
Ralph Chill, Mahamadi Warma
We put together a general framework to deal with elliptic and parabolic equations associated with (nonlinear) nonlocal (fractional order) operators. Many well-known nonlocal operat…
Domination of semigroups on standard forms of von Neumann algebras
Sahiba Arora, Ralph Chill, Sachi Srivastava
Consider and as real -semigroups generated by closed and symmetric sesquilinear forms on a standard form of a von Neumann algebra. We provide…
Real interpolation of functions with applications to accretive operators on Banach spaces
Ralph Chill, Praveen Sharma, Sachi Srivastava
We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in We show the equivalence of…
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions
Ralph Chill, Timo Reis, Tatjana Stykel
We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the…
Domination of semigroups generated by regular forms
Sahiba Arora, Ralph Chill, Jean-Daniel Djida
We give a representation for regular forms associated with dominated -semigroups which, in turn, characterises domination of -semigroups associated with regular forms. In…
Note on the Kato property of sectorial forms
Ralph Chill, Sebastian Krol
We characterise the Kato property of a sectorial form , defined on a Hilbert space , with respect to a larger Hilbert space in terms of two bounded, selfadjoin…
Semi-uniform stability of operator semigroups and energy decay of damped waves
R. Chill, D. Seifert, Y. Tomilov
Only in the last fifteen years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory o…
On the numerical range of second order elliptic operators with mixed boundary conditions in
Ralph Chill, Hannes Meinlschmidt, Joachim Rehberg
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide unifor…
Non-uniform Stability of Damped Contraction Semigroups
Ralph Chill, Lassi Paunonen, David Seifert +2
We investigate the stability properties of strongly continuous semigroups generated by operators of the form , where is a generator of a contraction semigroup and $B…
Atomic operators in vector lattices
Ralph Chill, Marat Pliev
In this paper we introduce a new class of operators on vector lattices. We say that a linear or nonlinear operator from a vector lattice to a vector lattice is atomic i…
Interpolation of nonlinear positive or order preserving operators on Banach lattices
Ralph Chill, Alberto Fiorenza, Sebastian Krol
We study the relationship between exact interpolation spaces for positive, linear operators, for order preserving, Lipschitz continuous operators, and for positive Gagliardo-Peetre…
The bidomain problem as a gradient system
Zakaria Belhachmi, Ralph Chill
We consider a general, nonlinear version of the bidomain system. Using the gradient structure of this system, but also the notion of -subgradient, we prove wellposedness of the…
The Kurdyka-Łojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems
Ralph Chill, Sebastian Mildner
We state and prove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite dimensional Hilbert spaces. One feature…
Weak and strong approximation of semigroups on Hilbert spaces
R. Chill, A. F. M. ter Elst
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence…
Operators and the norm continuity problem for semigroups
R. Chill, Yu. Tomilov
We present a new method for constructing -semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator-norm top…
The Laplace operator on the Sierpinski gasket with Robin boundary conditions
Brigitte E. Breckner, Ralph Chill
We study the Laplace operator on the Sierpinski gasket with nonlinear Robin boundary conditions. We show that for certain Robin boundary conditions the Laplace operator generates a…
Quantified versions of Ingham's theorem
Ralph Chill, David Seifert
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 th…
Real interpolation with weighted rearrangement invariant Banach function spaces
Ralph Chill, Sebastian Krol
Motivated by recent applications of weighted norm inequalities to maximal regularity of first and second order Cauchy problems, we study real interpolation spaces on the basis of g…
Application of the -subgradient in a problem of electropermeabilisation
Ralph Chill, Zakaria Belhachmi
We study a coupled elliptic-parabolic Poincaré-Steklov system arising in electrical cell activity in biological tissues. By using the notion of -subgradient, we show that this s…
Nonlinear semigroups generated by -elliptic functionals
Ralph Chill, Daniel Hauer, James B. Kennedy
We generalise the theory of energy functionals used in the study of gradient systems to the case where the domain of definition of the functional cannot be embedded into the Hilber…
Weighted inequalities for singular integral operators on the half-line
Ralph Chill, Sebastian Krol
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 weight…
Maximal regularity in interpolation spaces for second order Cauchy problems
Charles J. K. Batty, Ralph Chill, Sachi Srivastava
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 max…
Fine scales of decay of operator semigroups
Charles Batty, Ralph Chill, Yuri Tomilov
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and…
Uniqueness theorems for (sub-)harmonic functions with applications to operator theory
A. Borichev, R. Chill, Yu. Tomilov
We obtain uniqueness theorems for harmonic and subharmonic functions of a new type. They lead to new analytic extension criteria and new conditions for stability of operator semigr…