Veröffentlichungen

D. Knees and C. Zanini, “Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads,” Discrete and Continuous Dynamical Systems. Series S, vol. 14, no. 1, pp. 121–149, 2021.
http://dx.doi.org/10.3934/dcdss.2020332
D. Knees and V. Shcherbakov, “A penalized version of the local minimization scheme for rate-independent systems,” Applied Mathematics Letters, vol. 115, p. 106954, 2021.
http://dx.doi.org/10.1016/j.aml.2020.106954
D. Knees, “Convergence analysis of time-discretisation schemes for rate-independent systems,” ESAIM: Control, Optimisation and Calculus of Variations, p. TBD, 2018.
http://dx.doi.org/10.1051/cocv/2018048
D. Knees, R. Rossi, and C. Zanini, “Balanced viscosity solutions to a rate-independent system for damage,” European Journal of Applied Mathematics, vol. 146, pp. 1–59, 2018.
http://dx.doi.org/10.1017/S0956792517000407
H. Hanke and D. Knees, “A phase-field damage model based on evolving microstructure,” Asymptotic Analysis, vol. 101, no. 3, pp. 149–180, 2017.
http://dx.doi.org/10.3233/ASY-161396
R. Haller-Dintelmann, A. Jonsson, D. Knees, and J. Rehberg, “Elliptic and parabolic regularity for second-order divergence operators with mixed boundary conditions,” Mathematical Methods in the Applied Sciences, vol. 39, no. 17, pp. 5007–5026, 2016.
http://dx.doi.org/10.1002/mma.3484
H. Hanke and D. Knees, “Homogenization of elliptic systems with non-periodic, state-dependent coefficients,” Asymptotic Analysis, vol. 92, no. 3–4, pp. 203–234, 2015.
http://dx.doi.org/10.3233/ASY-141271
D. Knees, R. Rossi, and C. Zanini, “A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains,” Nonlinear Analysis: Real World Applications, vol. 24, pp. 126–162, 2015.
http://dx.doi.org/10.1016/j.nonrwa.2015.02.001
D. Knees, R. Kornhuber, C. Kraus, A. Mielke, and J. Sprekels, “C3: Phase transformation and separation in solids,” in MATHEON – Mathematics for Key Technologies, P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, C. Schütte, M. Skutella, and J. Sprekels, Eds. Zürich: European Mathematical Society Publishing House, 2014, pp. 189–203.
D. Knees and A. Schröder, “Computational aspects of quasi-static crack propagation,” Discrete and Continuous Dynamical Systems. Series S, vol. 6, no. 1, pp. 63–99, 2013.
http://dx.doi.org/10.3934/dcdss.2013.6.63
D. Knees, A. Fiaschi, and S. Reichelt, “Global higher integrability of minimizers of variational problems with mixed boundary conditions,” Journal of Mathematical Analysis and Applications, vol. 401, no. 1, pp. 269–288, 2013.
http://dx.doi.org/10.1016/j.jmaa.2012.11.040
D. Knees, R. Rossi, and C. Zanini, “A vanishing viscosity approach to a rate-independent damage model,” Mathematical Models and Methods in Applied Sciences, vol. 23, no. 4, pp. 565–616, 2013.
http://dx.doi.org/10.1142/S021820251250056X
D. Knees and A. Schröder, “Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints.,” Mathematical Methods in the Applied Sciences, vol. 35, no. 15, pp. 1859–1884, 2012.
http://dx.doi.org/10.1002/mma.2598
D. Knees, A. Fiaschi, and U. Stefanelli, “Young-measure quasi-static damage evolution,” Archive for Rational Mechanics and Analysis, vol. 203, no. 2, pp. 415–453, 2012.
http://dx.doi.org/10.1007/s00205-011-0474-3
D. Knees, “Global spatial regularity for a regularized elasto-plastic model,” GAMM-Mitteilungen / GAMM-Reports, vol. 34, no. 1, pp. 21–27, 2011.
http://dx.doi.org/10.1002/gamm.201110003
D. Knees, C. Zanini, and A. Mielke, “Crack growth in polyconvex materials,” Physica D: Nonlinear Phenomena, vol. 239, no. 15, pp. 1470–1484, 2010.
http://dx.doi.org/10.1016/j.physd.2009.02.008
D. Knees, “On global spatial regularity and convergence rates for time-dependent elasto-plasticity.,” Mathematical Models and Methods in Applied Sciences, vol. 20, no. 10, pp. 1823–1858, 2010.
http://dx.doi.org/10.1142/S0218202510004805
P. G. Gruber, D. Knees, S. Nesenenko, and M. Thomas, “Analytical and numerical aspects of time-dependent models with internal variables.,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 90, no. 10–11, pp. 861–902, 2010.
http://dx.doi.org/10.1002/zamm.200900387
D. Knees, “On global spatial regularity in elasto-plasticity with linear hardening,” Calculus of Variations and Partial Differential Equations, vol. 36, no. 4, pp. 611–625, 2009.
http://dx.doi.org/10.1007/s00526-009-0247-0
D. Knees, A. Mielke, and C. Zanini, “On rate independent models for crack propagation,” PAMM, vol. 8, no. 1, pp. 10213–10214, 2008.
http://dx.doi.org/10.1002/pamm.200810213
D. Knees, A. Mielke, and C. Zanini, “On the inviscid limit of a model for crack propagation.,” Mathematical Models and Methods in Applied Sciences, vol. 18, no. 9, pp. 1529–1569, 2008.
http://dx.doi.org/10.1142/S0218202508003121
P. Neff and D. Knees, “Regularity up to the boundary for nonlinear elliptic systems arising in time-incremental infinitesimal elasto-plasticity,” SIAM Journal on Mathematical Analysis, vol. 40, no. 1, pp. 21–43, 2008.
http://dx.doi.org/10.1137/070695824
D. Knees, “Global stress regularity of convex and some nonconvex variational problems,” Annali di Matematica Pura ed Applicata. Serie Quarta, vol. 187, no. 1, pp. 157–184, 2008.
http://dx.doi.org/10.1007/s10231-006-0039-5
D. Knees and A. Mielke, “Energy release rate for cracks in finite-strain elasticity.,” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 5, pp. 501–528, 2008.
http://dx.doi.org/10.1002/mma.922
D. Knees and A.-M. Sändig, “Regularity of elastic fields in composites.,” in Multifield problems in solid and fluid mechanics, R. Helmig, A. Mielke, and B. I. Wohlmuth, Eds. Berlin: Springer, 2006, pp. 331–360.
http://dx.doi.org/10.1007/978-3-540-34961-7_10
D. Knees, “Griffith-formula and J-integral for a crack in a power-law hardening material,” Mathematical Models and Methods in Applied Sciences, vol. 16, no. 11, pp. 1723–1749, 2006.
http://dx.doi.org/10.1142/S0218202506001698
D. Knees, “Global regularity of the elastic fields of a power-law model on Lipschitz domains,” Mathematical Models and Methods in Applied Sciences, vol. 29, no. 12, pp. 1363–1391, 2006.
http://dx.doi.org/10.1002/mma.727
D. Knees and A.-M. Sändig, “Stress behaviour in a power-law hardening material,” in Proceedings of the Conference held in Milvoy, Bohemiam-Moravian Uplands, May 28-June 2, 2004, P. Drábek and J. Rákosník, Eds. Prag: Mathematical Institute of the Academy of Sciences of the Czech Republic, 2005, pp. 134–151.
D. Knees, “On the Regularity of Weak Solutions of Quasi-Linear Elliptic Transmission Problems on Polyhedral Domains,” Zeitschrift für Analysis und ihre Anwendungen, vol. 23, no. 3, pp. 509–546, 2004.
http://dx.doi.org/10.4171/ZAA/1209

https://www.mathematik.uni-kassel.de/~dknees/publications/knees03_2.pdf
D. Knees, “Regularity results for transmission problems of linear elasticity on polyhedral domains.,” in Analysis and Simulation of Multifield Problems, W. L. Wendland and M. Efendiev, Eds. Berlin: Springer, 2003, pp. 221–226.
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Meyer, C., Knees, D., Herzog, R. (Eds.), 2018. Nonsmooth Models in Continuum Mechanics - Analysis and Optimization, GAMM-Mitteilungen. Wiley-VCH GmbH, Weinheim. https://doi.org/10.1002/gamm.201730001
Kaiser, H.-C., Knees, D., Mielke, A., Rehberg, J., Rocca, E., Thomas, M., Valdinoci, E. (Eds.), 2017. Special issue on PDE 2015: Theory and applications of partial differential equations, Discrete and Continuous Dynamical Systems. Series S. American Institute of Mathematical Sciences, Springfield, USA. https://doi.org/10.3934/dcdss.201704i
Klein, O., Knees, D., Dimian, M., Rachinskii, D., Gurevich, P., Tikhomirov, S. (Eds.), 2016. MURPHYS-HSFS-2014: 7th international workshop on MUlti-Rate Processes & HYSteresis (MURPHYS) and the 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany, April 7-11, 2014., Journal of Physics: Conference Series. IOP Publishing, Bristol. https://doi.org/10.1088/1742-6596/727/1/011001