# Publications

Books

Peer reviewed articles and preprints

Memoirs

## BOOKS

- W. Arendt, R. Chill and Y. Tomilov (eds.),
**“Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics,”**Proceedings of the conference held in Herrnhut, June 2013, Operator Theory, Advances and Applications, vol. 250, Birkhäuser Verlag, Basel, 2015. - R. Chill and E. Fasangova,
**“Gradient Systems,”**Lecture Notes of the 13th International Internet Seminar, Matfyzpress, Prague, 2010.

## Peer reviewed articles and preprints

- R. Chill, T. Reis and T. Stykel,
**“Analysis of a quasilinear coupled magneto-quasistatic model. Part I: Solvability and regularity of solutions****,”***Preprint, 2021**.* - R. Chill, L. Paunonen, D. Seifert, R. Stahn and Y. Tomilov,
**“Nonuniform stability of damped contraction semigroups,”***Preprint, 2019**.* - R. Chill and S. Krol,
**“Note on the Kato property of sectorial forms,”***J. Operator Theory, to appear**.* - R. Chill, H. Meinlschmidt and J. Rehberg,
**“On the numerical range of second order elliptic operators with mixed boundary conditions in $L^p$,”***J. Evolution Equations, to appear**.* - R. Chill, D. Seifert and Y. Tomilov,
**“Semi-uniform stability of $C_0$-semigroups and energy decay of damped waves,”***Philos. Trans. Roy. Soc. A*378 (2020), no. 2185, 20190614, 24 pp*.* - R. Chill and M. Pliev,
**“Atomic operators on vector lattices,”***Mediterranean J. Math. 17, Art. no. 138 (2020), 21 pp.* - R. Chill, A. Fiorenza and S. Krol,
**“Interpolation of nonlinear order preserving operators on Banach lattices,”***Positivity 24(3) (2020), 507-532.* - Z. Belhachmi and R. Chill,
**“The bidomain problem as a gradient systems****,”***J. Differential Equations 268 (2020), 6598-6610.* - R. Chill and M. Warma,
**“Corrigendum to: Dirichlet and Neumann boundary conditions for the $p$-Laplace operator: What is in between?”***Proc. Royal Soc. Edinburgh, Sect A*149 (2019), 1689-1691. - R. Chill and S. Mildner,
**“The Kurdyka-Lojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems****,”***Proc. Amer. Math. Soc 146 (2018), no. 10, 4307-4014*. - R. Chill and S. Krol,
**“****Weighted inequalities for singular integral operators on the half-line,”***Studia Math.**243 (2018), no. 2, 171-206*. - R. Chill and A.F.M. ter Elst,
**“****Weak and strong approximation of semigroups on Hilbert spaces,”***Integral Equations Operator Theory*90 (2018), no. 1, 90:9. - R. Chill and S. Krol,
**“Extrapolation of L**^{p}-maximal regularity for second order Cauchy problems,”*Banach Center Publications 112 (2017), 33-52*. - G. Anatriello, R. Chill and A. Fiorenza,
**“****Identification of fully measurable grand Lebesgue spaces,”***J. Function Spaces 2017, Art. ID 3129186, 3 pp**.* - B. Breckner and R. Chill,
**“****The Laplace operator on the Sierpinski gasket with Robin boundary conditions,”***Nonlinear Anal. Real World Appl. 38 (2017), 245-260*. - R. Chill and S. Krol,
**“****Real interpolation with weighted rearrangement invariant Banach function spaces,”***J. Evol. Eq.*17 (2017), 173-195. - R. Chill and D. Seifert,
**“****Quantified versions of Ingham's theorem,”***Bull. London Math. Soc.**48 (2016), 519-532.* - C.J.K. Batty, R. Chill and Y. Tomilov
**, “Fine scales of decay of operator semigroups,”***J. Europ. Math. Soc 18 (2016), 853-929.* - R. Chill, D. Hauer and J. Kennedy,
**“****Nonlinear semigroups generated by $j$-elliptic functionals,”***J. Math. Pures Appl.*105 (2016), 415-450. - Z. Belhachmi and R. Chill,
**“****Application of the j-subgradient in a problem of electropermeabilisation,”***J. Elliptic Parabolic Equations 1 (*2015), 13-29. - C.J.K. Batty, R. Chill and S. Srivastava,
**“Maximal regularity in interpolation spaces for second order Cauchy problems,”***Operator semigroups meet complex analysis, harmonic analysis and mathematical physics, Proceedings of the conference held in Herrnhut, June 2013*, 2015, pp. 49-66.*(W. Arendt, R. Chill and Y. Tomilov eds.)*, Operator Theory, Advances and Applications, vol. 250, Birkhäuser Verlag - R. Chill and A. Fiorenza,
**“Singular integral operators with operator-valued kernels, and extrapolation of maximal regularity into rearrangement invariant Banach function spaces,”***J. Evol. Eq.*14 (2014), 795-828. - R. Chill and M. Warma,
**“A Riesz type representation for lower semi-continuous, monotone, local functionals on $C_c (X)^+$,”***Nonlinear Analysis*85 (2013), 17-22. - R. Chill and M. Warma,
**“Dirichlet and Neumann boundary conditions for the $p$-Laplace operator: What is in between?”***Proc. Royal Soc. Edinburgh, Sect A*142 (2012), 975-1002. - S. Boussandel, R. Chill and E. Fasangova,
**“Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow,”***Czechoslovak Math. J.*62 (2) (2012), 335-346. - T. Barta, R. Chill and E. Fasangova,
**“Every ordinary differential equation with a strict Lyapunov function is a gradient system,”***Monatsh. Math.*, no. 166 (1) (2012), 57-72. - R. Chill and W. Radzki,
**“Stabilization of solutions of dissipative Hamiltonian systems,”***J. Math. Anal. Appl.*, no. 380 (2), 2011, 750-758. - W. Arendt and R. Chill,
**“Global existence for quasilinear diffusion equations in isotropic nondivergence form,”***Ann. Sc. Norm. Super. Pisa Cl. Sci.*, no. 9 (3), 2010, 523-539. - R. Chill, A. Haraux and M. A. Jendoubi,
**“Applications of the Lojasiewicz-Simon gradient inequality to gradient-like evolution equations,”***Anal. Appl.*, no. 7, 2009, pp. 351-372. - R. Chill, E. Fasangova and R. Schätzle,
**“Willmore blow-ups are never compact,”***Duke Math. J.*, no. 147, 2009, pp. 345-376. - R. Chill and Yuri Tomilov,
**“Operators $L^1(\R) \to X$ and the norm continuity problem for semigroups,”***J. Funct. Anal.*, no. 256, 2009, 352-384. - R. Chill,
**“Three variations on Newton's method,”***Math. Student*, no. 77, 2008, 213-229. - C.J.K. Batty, R. Chill and S. Srivastava,
**“Maximal regularity for second order non-autonomous Cauchy problems,”***Studia Math.*, no. 256, 2008, 205-223. - R. Chill and S. Srivastava,
**“$L^p$-maximal regularity for second order Cauchy problems is independent of $p$,”***Boll. Unione Mat. Ital. Ser. IX*, no. 1, 2008, pp. 147-158. - R. Chill, V. Keyantuo and M. Warma,
**“Generation of cosine families on $L^p (0,1)$ by elliptic operators with Robin boundary conditions ,”***Functional Analysis and Evolution Equations. The Günter Lumer Volume. (H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Below (eds.)*, 2008, pp. 113-130. - A. Borichev, R. Chill and Y. Tomilov,
**“Uniqueness theorems for (sub-)harmonic functions with applications to operator theory,”***Proc. London Math. Soc.*, no. 95, 2007, pp. 687-708. - R. Chill and M. A. Jendoubi,
**“Convergence to steady states of solutions of non-autonomous heat equations in $R^N$,”***J. Dynam. Differential Equations*, no. 19, 2007, pp. 777-788. - W. Arendt, R. Chill, S. Fornaro and C. Poupaud,
**“$L^p$-maximal regularity for non-autonomous evolution equations,”***J. Differential Equations*, no. 237, 2007, pp. 1-26. - R. Chill and Y. Tomilov,
**“Stability of operator semigroups: ideas and results,”***Banach Center Publications*, no. 75, 2007, pp. 71-109. - R. Chill,
**“The Lojasiewicz-Simon gradient inequality in Hilbert spaces ,”***Proceedings of the 5th European-Maghrebian Workshop on Semigroup Theory, Evolution Equations, and Applications (M. A. Jendoubi, ed.)*, 2006, pp. 25-36. - R. Chill and A. Fiorenza,
**“Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations,”***J. Differential Equations*, no. 228, 2006, pp. 611-632. - R. Chill, E. Fasangova, G. Metafune and D. Pallara,
**“The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators,”***C. R. Acad. Sci. Paris*, no. 342, 2006, pp. 909-914. - R. Chill, E. Fasangova and J. Prüss,
**“Convergence to steady states of solutions of the Cahn-Hilliard and Caginalp equations with dynamic boundary conditions,”***Math. Nachr.*, no. 279, 2006, 1448-1462. - R. Chill and S. Srivastava,
**“$L^p$-maximal regularity for second order Cauchy problems,”***Math. Z.*, no. 251, 2005, pp. 751-781. - R. Chill, E. Fasangova, G. Metafune and D. Pallara,
**“The sector of analyticity of the Ornstein-Uhlenbeck semigroup in $L^p$ spaces with respect to invariant measure,”***J. London Math. Soc.*, no. 71, 2005, pp. 703-722. - R. Chill and E. Fasangova,
**“Convergence to steady states of solutions of semilinear evolutionary integral equations,”***Calc. Var. Partial Differential Equations*, no. 22, 2005, pp. 321-342. - R. Chill and Y. Tomilov,
**“Analytic continuation and stability of operator semigroups,”***J. Analyse Math.*, no. 93, 2004, pp. 331-358. - R. Chill and A. Haraux,
**“An optimal estimate for the time singular limit of an abstract wave equation,”***Funkcialaj Ekvac.*, no. 47, 2004, pp. 277-290. - R. Chill and A. Haraux,
**“An optimal estimate for the difference of solutions of two abstract evolution equations,”***J. Differential Equations*, no. 193, 2003, pp. 385-395. - S. Bu and R. Chill,
**“A remark about the interpolation of spaces of continuous, vector-valued functions,”***J. Math. Anal. Appl.*, no. 288, 2003, pp. 246-250. - R. Chill,
**“On the Lojasiewicz-Simon gradient inequality,”***J. Funct. Anal.*, no. 201, 2003, pp. 572-601. - R. Chill and M. A. Jendoubi,
**“Convergence to steady states in asymptotically autonomous semilinear evolution equations,”***Nonlinear Analysis, TMA*, no. 53, 2003, pp. 1017-1039. - R. Chill and Y. Tomilov,
**“Stability of $C_0$-semigroups and geometry of Banach spaces,”***Math. Proc. Cambridge Phil. Soc.*, no. 135, 2003, pp. 493-511. - R. Chill,
**“Convergence of bounded solutions to gradient-like semilinear Cauchy problems with radial nonlinearity,”***Asymptotic Anal.*, no. 33, 2003, pp. 93-106. - S. Bu and R. Chill,
**“Banach spaces with the Riemann-Lebesgue or the analytic Riemann-Lebesgue property,”***Bull. London Math. Soc.*, no. 34, 2002, pp. 569-581. - R. Chill,
**“Operators $C_0(\R;Y) \to X$ and asymptotic behaviour of abstract delay equations,”***Revue Roumaine Math. Pures Appl.*, no. 48, 2003, pp. 31-54. - C.J.K. Batty and R. Chill,
**“Approximation and asymptotic behaviour of evolution families,”***Differential Integral Equations*, no. 15, 2002, pp. 477-512. - R. Chill and E. Fasangova,
**“Equality of two spectra arising in harmonic analysis and semigroup theory,”***Proc. Amer. Math. Soc.*, no. 130, 2002, pp. 675-681. - C.J.K. Batty, R. Chill and Y. Tomilov,
**“Strong stability of bounded evolution families and semigroups,”***J. Funct. Anal.*, no. 193, 2002, pp. 116-139. - R. Chill and J. Prüss,
**“Asymptotic behaviour of evolutionary integral equations,”***Int. Eq. Operator Theory*, no. 39, 2001, pp. 193-213. - C.J.K. Batty, R. Chill and J. van Neerven,
**“ Asymptotic behaviour of $C_0$-semigroups with bounded local resolvents,”***Math. Nachr.*, no. 219, 2000, pp. 65-83. - C.J.K. Batty and R. Chill,
**“Bounded convolutions and solutions of inhomogeneous Cauchy problems,”***Forum Math.*, no. 11 (2), 1999, pp. 253-277. - R. Chill,
**“Tauberian theorems for vector-valued Fourier and Laplace transforms,”***Studia Math.*, no. 128, 1998, pp. 55-69. - R. Chill,
**“Stability results for individual solutions of the abstract Cauchy problem via Tauberian theorems,”***Ulmer Seminare über Funktionalanalysis und Differentialgleichungen*, no. 1, 1996, pp. 122-133.

## Memoirs

- R. Chill,
*Fourier transforms and asymptotics of evolution equations*, Dissertation, Universität Ulm, 1998. - R. Chill,
*Taubersche Sätze und Asymptotik des abstrakten Cauchy-Problems*, Diplomarbeit, Universität Tübingen, 1995.