Publications & Preprints of Dorothee Knees

Publications

• D. Knees, S. Thomas, Optimal control of a rate-independent system constrained to parametrized balanced viscosity solutions, SIAM Journal on Control and OptimizationVolume 61, Issue 2, pp. 361-923, 2023. (arXiv, SIAM)
• D. Knees, S. Owczarek, P. Neff, A local regularity result for the relaxed micromorphic model based on inner variations, J. Math. Anal. Appl. 519, Issue 2, 15 March 2023, 126806, arXiv:2208.04821, 2022. (pdf)
• D. Knees, C. Meyer, M. Sievers, Optimal control of non-convex rate-independent systems via vanishing viscosity – The finite dimensional case. Pure Appl. Funct. Anal. 7, No. 5, 1733-1766 (2022). (link)
• D. Knees, A, Schröder, V. Shcherbakov, Fully discrete approximation schemes for rate-independent crack evolution, Philosophical Transactions A, issue on “Non-smooth variational problems and applications”, published online on 26th September 2022.
• R, Herzog, D. Knees, C. Meyer, M. Sievers, A. Stötzner, S. Thomas Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control, in: M. Hintermüller, R. Herzog, C. Kanzow, M. Ulbrich, S. Ulbrich (eds.), Non-smooth and complementarity-based distributed parameter systems. Simulation and hierarchical optimization. ISNM. International Series of Numerical Mathematics 172. Cham: Birkhäuser, 2022. (link)
• D. Knees, V. Shcherbakov, A penalized version of the local minimization scheme for rate-independent systems, Appl. Math. Lett. 115, Article ID 106954, 2021. (link)
• D. Knees, C. Zanini, Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads, Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 121-149, 2021. (pdf)
• D. Knees, Convergence analysis of time-discretisation schemes for rate-independent systems,
  ESAIM, Control Optim. Calc. Var., vol. 25, article 65, 2019.
  DOI: https://doi.org/10.1051/cocv/2018048. (pdf)
• D. Knees, R. Rossi, C. Zanini Balanced Viscosity solutions to a rate-independent system for damage,
  Eur. J. Appl. Math., vol. 30, pp. 117-175, 2019; (published online Jan 2018). (pdf)
• D. Knees, M. Negri, Convergence of alternate minimization schemes for phase field fracture and damage,
  Mathematical Models and Methods in Applied Sciences (M3AS), vol. 27(9), pp. 1743-1794, 2017. (pdf)
• H.-Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci (eds.), PDE 2015: Theory and Applications of Partial Differential Equations,
  proceedings of PDE 2015, DCDS-S Discrete Contin. Dyn. Syst. Ser. S, vol. 10(4), 2017.
• H. Hanke, D.Knees, A phase-field damage model based on evolving microstructure,
  Asymptotic Analysis, vol. 101(3), pp. 149-180, 2017. (pdf)
• R. Haller-Dintelmann, A. Jonsson, D. Knees, J. Rehberg, Elliptic and parabolic regularity for second order divergence operators with mixed boundary conditions.
  Mathematical Methods in the Applied Sciences, vol. 39(17), pp. 5007-5026, 2016. (pdf, accepted version)
• D. Knees, R. Rossi, Ch. Zanini, A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains,
  Nonlinear Analysis Series B: Real World Applications, vol. 24, pp. 126-162 , 2015. (pdf, article)
• H. Hanke, D. Knees, Homogenization of elliptic systems with non-periodic, state dependent coefficients,
  Asymptotic Analysis, vol. 92,pp. 203-234, 2015. (pdf)
• D. Knees, R. Kornhuber, Chr. Kraus, A. Mielke, J. Sprekels. C3 -- Phase transformation and separation in solids. "MATHEON -- Mathematics for Key Technologies" in EMS Series in Industrial and Applied Mathematics, vol. 1(1): 189-203, 2014.
• D. Knees, R. Rossi, C. Zanini, A vanishing viscosity approach to a rate-independent damage model,
  Mathematical Models and Methods in Applied Sciences, vol.23(04), pp. 565-616, 2013. (preprint)
• A. Fiaschi, D. Knees, S. Reichelt, Global higher integrability of minimizers of variational problems with mixed boundary conditions,
  Journal of Mathematical Analysis and Applications, vol. 401, pp. 269-288, 2013. (pdf)
• D. Knees, A. Schröder, Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints,
  Mathematical Methods in the Applied Sciences. Special Issue: Perspectives in Continuum Mechanics, vol. 35(15), pp. 1859-1884, 2012. (pdf)
• D. Knees, A. Schröder, Computational aspects of quasi-static crack propagation,
  Discrete and Continuous Dynamical Systems - Series S (DCDS-S), vol. 6(1), pp. 63-99, 2013. (pdf)
• A. Fiaschi, D. Knees, U. Stefanelli, Young measure quasi-static damage evolution,
  Arch. Rational Mech. Anal., vol. 203(2), pp. 415-453, 2012.
• D. Knees, Global spatial regularity for a regularized elasto-plastic model,
  GAMM-Mitteilungen, vol. 34(1), pp. 21-27,2011.
• D. Knees, On global spatial regularity and convergence rates for time dependent elasto-plasticity,
  Mathematical Models and Methods in Applied Sciences (M3AS). vol. 20(10), pp. 1823-1858, 2010. (Preprint)
• P. Gruber, D. Knees, S. Nesenenko, M. Thomas, Analytical and numerical aspects of time-dependent problems with internal variables,
  ZAMM, Z. Angew. Math. Mech., vol. 90(10-11), pp. 861-902, 2010. (pdf)
• D. Knees, C. Zanini, A. Mielke, Crack growth in polyconvex materials,
  Physica D, vol. 239(15), pp. 1470 - 1484 2010. (Preprint)
• D. Knees, On global spatial regularity in elasto-plasticity with linear hardening,
  Calculus of Variations and Partial Differential Equations, vol.36(4), pp. 611-625, 2009. (Preprint)
• D. Knees, A. Mielke, C. Zanini, On the inviscid limit of a model for crack propagation,
  Mathematical Models and Methods in Applied Sciences, vol. 18(9), pp. 1529 - 1569, 2008. (Preprint)
• D. Knees, P. Neff, Regularity up to the boundary for nonlinear elliptic systems arising in time-incremental infinitesimal elasto-plasticity,
  SIAM Journal on Math. Analysis, vol. 40(1), pp. 21-43, 2008. (Preprint)
• D. Knees, A. Mielke, On the energy release rate in finite-strain elasticity,
  Mechanics of Advanced Materials and Structures, vol. 15(6), pp. 421-427, 2008.
• D. Knees, A. Mielke, Energy release rate for cracks in finite-strain elasticity,
  Mathematical Methods in the Applied Sciences, vol. 31(5), pp. 501-528, 2008. (Preprint)
• D. Knees, Global stress regularity for convex and some nonconvex variational problems on Lipschitz domains,
  Annali di Matematica Pura ed Applicata, vol.187, pp.157-184, 2008. (Preprint)
• D. Knees, Griffith-formula and J-integral for a crack in a power-law hardening material,
  Mathematical Models and Methods in Applied Sciences (M3AS), vol. 16, no.11, p. 1723-1749, 2006. (Preprint)
• D. Knees, A.-M. Sändig, Regularity of Elastic Fields in Composites,
  in: Multifield Problems in Solid and Fluid Mechanics (R. Helmig, A. Mielke and B. Wohlmuth, eds.). Lecture Notes in Applied and Computational Mechanics , Vol. 28, Springer-Verlag, p. 321-350, 2006. (pdf)
• D. Knees, Global regularity of the elastic fields of a power-law model on Lipschitz domains,
  Mathematical Methods in the Applied Sciences, vol. 29, p. 1363-1391, 2006. DOI: 10.1002/mma.727. (Preprint)
• D. Knees, A.-M. Sändig, Stress behaviour in a power-law hardening material,
  in: Function Spaces, Differential Operators, and Nonlinear Analysis (P. Drábek and J. Rákosník eds.), Proceedings of the Conference held in Milvoy, Bohemiam-Moravian Uplands, May 28-June 2, 2004; Mathematical Institute of the Academy of Sciences of the Czech Republic, Praha, p. 134-151, 2005.
• D. Knees, On the regularity of weak solutions of nonlinear transmission problems on polyhedral domains,
  Zeitschrift für Analysis und ihre Anwendungen, vol. 23, no. 3, pp. 509-546, 2004. (Preprint)
• D. Knees, Regularity results for transmission problems of linear elasticity on polyhedral domains,
  in: Analysis and simulation of multifield problems (M. Efendiev, W.L. Wendland, eds.), Springer Verlag, 2003.

Editor of

• Issue on PDE 2015: Theory and applications of partial differential equations,
  Discrete Contin. Dyn. Syst. Ser. S, 10, No.4 (2017), edited by H.-C. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci.
• Nonsmooth Models in Continuum Mechanics - Analysis and Optimization, GAMM-Mitteilungen, 40, No. 3-4 (2018), edited by C. Meyer, D. Knees, R. Herzog.

Preprints

• F. Rörentrop, S. Boddin, D. Knees, J. Mosler, A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics arXiv:2403.07461, 2024. (pdf)
• D. Knees, P. Neff, S. Owczarek, A global higher regularity result for the static relaxed micromorphic model on smooth domains, arXiv:2307.02621, 2023. (pdf)
• S. Boddin, F. Rörentrop, D. Knees, J. Mosler, Approximation of balanced viscosity solutions of a rate-independent damage model by combining alternate minimization with a local minimization algorithm, arXiv:2211.12940, 2022. (pdf)
• D. Knees, A.-M. Sändig (Hrsg.), Nichtlineare Funktionalanalysis mit Anwendungen in der Festkörpermechanik,
  Universität Stuttgart, IANS, Seminarbericht 2004/011 , 2004.
• D. Knees, On the regularity of weak solutions of a shear thinning fluid of power-law type,
  SFB 404, Bericht 2003/23.
• D. Knees, Regularity results for transmission problems for the Laplace and Lamé operators on polygonal or polyhedral domains,
  SFB 404, Bericht 2002/10.

PhD thesis
Regularity results for quasilinear elliptic systems of power-law growth in nonsmooth domains
–Boundary, transmission and crack problems–,
University of Stuttgart, 2005. (pdf)

Diploma thesis
Regularitätsaussagen für zweidimensionale elastische Felder in Kompositen,
University of Stuttgart, 2001. (ps)

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Last modified: 2024-03-15 by Dorothee Knees