Department Mathematik



Publications of Prof. Dr. Lars Diening


[B1] L. Diening, P. Hästo, P. Harjulehto, M. Ruzicka: Lebesgue and Sobolev spaces with variable exponents, Springer Lecture Notes, vol. 2017, Springer-Verlag, Berlin 2011. Download complete preprint (PDF), Final version from Springer.

All Publications

[65] S. Dahlke, L.. Diening, C. Hartmann, B. Scharf, M. Weimar: Besov regularity of solutions to the p-Poisson equation Submitted. 2014. arXiv preprint.
[64] D. Breit, L. Diening, L. Berselli: Convergence Analysis for a Finite Element Approximation of a Steady Model for Electrorheological Fluids. Submitted. 2014. arXiv preprint.
[63] D. Breit, L. Diening, S. Schwarzacher: Finite element approximation of the p(.)-Laplacian. Siam J. Numerical Analysis, 2015, vol. 53, no. 1, pp. 551-572. arXiv preprint.
[62] L. Diening, S. Schwarzacher: Global gradient estimates for the p(.)-Laplacian, arXiv preprint. Nonlinear Analysis: Theory, Methods & Applications, 2014, no 106, pp. 70-85.
[61] L. C. Berselli, L. Diening, M. Ruzicka: Optimal error estimate for semi-implicit space-time discretization for the equations describing incompressible generalized Newtonian fluids. IMA Journal of Numerical Analysis, 2014, article. arXiv preprint.
[60] H. Abels, L. Diening, Y. Terasawa: Existence of weak solutions for a diffuse in- terface model of power-law type two-phase flows. International Conference on Mathematical Fluid Dynamics on the occation of Professor Yoshihiro Shibata's 60th birthday, to appear in Mathematical Fluid Mechanics from Birkhauser-Verlag.
[59] L. Diening, Ch. Kreuzer, R. Stevenson: Instance optimality of the adaptive maximum strategy. Submitted. 2013. arXiv preprint. Foundations of Computational Mathematics, 2014, accepted.
[58] L. Diening, S. Schwarzacher: On the key estimate for variable exponent spaces. Azerbaijan Journal of Mathematics (2013) volume 3, number 2, pp. 75-82. Article
[57] L. Diening: Part 1: Discrete Sobolev spaces, Part 2: Lipschitz truncation; Lecture Notes of the Spring School of Analysis 2013 (Paseky).
[56] L. Diening: Lipschitz truncation and the p-Laplace. Oberwolfach Report 2013. Miniworkshop: The p-Laplacian Operator and Applications.
[55] H. Abels, L. Diening, Y. Terasawa: Existence of Weak Solutions for a Diffuse Interface Model of Non-Newtonian Two-Phase Flows. Nonlinear Analysis Series B: Real World Applications, Vol. 15, 2014, pp. 149-157. article. arXiv preprint
[54] L. Diening, P. Kaplicky, S. Schwarzacher: Campanato estimates for the generalized Stokes System. 2012. Annali di Matematica Pura ed Applicata. Accepted. arXiv preprint
[53] D. Breit, L. Diening, S. Schwarzacher: Solenoidal Lipschitz truncation for parabolic PDE’s. 2012. Mathematical Models and Methods in Applied Sciences (M3AS) Volume 23, Issue 14, 30 December 2013. DOI: 10.1142/S0218202513500437. arXiv preprint
[52] L. Diening, D. Kröner, M. Ruzicka, I. Toulopoulos: A Local Discontinuous Galerkin approximation for systems with p-structure. 2012. IMA Journal of Numerical Analysis. Accepted. Preprint
[51] L. Diening, Ch. Kreuzer, E. Süli: Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology. SIAM Journal on Numerical Analysis, 51(2), 984-1015 (2013). arXiv preprint
[50] L. Diening, P.  Kaplicky: Lq theory for a generalized Stokes System. Manuscripta Mathematica 2012. Online first. DOI 10.1007/s00229-012-0574-x May 2013, Volume 141, Issue 1-2, pp 333-361.
[49] L. Diening, D.  Lengeler, B. Stroffolini, A. Verde: Partial regularity for minimizers of quasiconvex functionals with general growth. SIAM J. MATH. ANAL., (2012) Vol. 44, No.5, pp. 3594-3616. Download, DOI 10.1137/120870554.
[48] L. Diening, Ch. Kreuzer, S. Schwarzacher: Convex Hull Property and Maximum Principles for Finite Element Minimizers of General Convex Functionals. (2012) Numerische Mathematik (online first), doi: 10.1007/s00211-013-0527-7. Preprint. arXiv preprint.
[47] D. Breit, L. Diening, M. Fuchs: Solenoidal Lipschitz truncation and applications in fluid, (2012) Journal of Differential Equations, 253, pp. 1910-1942.
[46] L. Diening, P. Kaplicky, S. Schwarzacher: BMO estimates for the p-Laplacian, Nonlinear Analysis: Theory, Methods & Applications, 2012, Vol. 75, 637-650, DOI 10.1016/, Preprint.
[45] L. Diening, D.. Cruz-Uribe, P. Hästö: Maximal function on weighted Lebesgue spaces with variable exponents, Fract. Calc. Appl. Anal. Vol. 14, No 3 (2011), pp. 361-374.
[44] D. Breit, L. Diening: Sharp conditions for Korn inequalities in Orlicz spaces, Journal of Mathematical Fluid Mechanics, (2012) 14, pp. 565-573, DOI: 10.1007/s00021-011-0082-x.
[43] L. Diening, P. Nägele, M. Ruzicka: Monotone operator theory for unsteady problems in variable exponent spaces, Complex Variables and Elliptic Equations, 2010, DOI 10.1080/17476933.2011.557157, (online since 19. September 2011).
[42] L. Belenki, L. Diening, Ch. Kreuzer: Optimality of an adaptive finite element method for the p-Laplacian equation, IMA Journal of Numerical Analysis (2012) 32(2), 484-510, DOI~10.1093/imanum/drr016. Artikel
[41] L. Belenki, L. Berselli, L. Diening, M. Ruzicka. On the finite element approximation of p-Stokes systems, SIAM Journal on Numerical Analysis, 2012, DOI: 10.1137/10080436X.
[40] L. Diening, D. Lengeler, M. Ruzicka: The Stokes and Poisson Problem in Variable Exponent Spaces, Com. Var. Ell. Equ. (2010). arXiv preprint. Com. Var. Ell. Equ. (2011) 56, No.7-9, 789 - 811; DOI 10.1080/17476933.2010.504843, (online seit: 11. Mai 2011). arXiv preprint.
[39] L. Diening, B. Stroffolini, and A. Verde: The phi-harmonic approximation and the regularity of phi-harmonic maps, J. Differential Equations 253 (2012), no. 7, 1943-1958. DOI 10.1016/j.jde.2012.06.010 .
[38] L. Diening, S. Samko: On potentials in generalized Hölder spaces over uniform domains in Rn, (2010) Revista Matematica Complutense, (2011) vol 24, no 2, 357-373.
[37] L. Diening, M. Ruzicka: An existence result for non-Newtonian fluids in non-regular domains, (2010). AIMS special issue, no 2, 255-268.
[36] P. Hästö, L. Diening : Muckenhoupt weights in variable exponent spaces, (2011), submitted. Preprint.
[35] L. Diening, B. Stroffolini, and A. Verde: Lipschitz regularity for some asymptotically convex problems, ESAIM Control Optim. Calc. Var. (2011), vol 17, no 1, 178-189.
[34] L. Diening, M. Ruzicka, K. Schumacher: A Decomposition technique for John domains, Technical Report 6/2008, University of Freiburg, (2009), Annales Academiae Scientiarum Fennicae, vol 35, 87-114.
[33] L. Diening, B. Stroffolini, and A. Verde: Everywhere Regularity of functionals with phi-growth, (2008). Manuscripta Mathematica, 129 (2009) Issue 4, DOI: 10.1007/s00229-009-0277-0.
[32] L. Diening, S. Fröschl: Extensions in spaces with variable exponents --- The half space. Proceedings of the RIMS Meeting on Harmonic Analysis and Nonlinear Partial Differential Equations (2008).
[31] L. Diening, M. Ruzicka, and J. Wolf: Existence of Weak Solutions for Unsteady Motions of Generalized Newtonian Fluids. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, IX, (2010), 1-46.
[30] L. Diening: Lebesgue and Sobolev Spaces with Variable Exponent. Habilitation (Postdoctoral thesis), Univ. Freiburg im Breisgau, Mathematische Fakultät, (2007), 173 pages.
[29] L. C. Berselli, L. Diening, and M. Ruzicka: Optimal estimates for a semi implicit euler scheme for incompressible fluids with shear dependent viscosities, Technial Report 7/2008, University of Pisa, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. DOWNLOAD PREPRINT. SIAM J. Numer. Anal. (2012). 50(2), DOI 10.1137/10080436X.
[28] L. C. Berselli, L. Diening, and M. Ruzicka. Existence of strong solutions for incompressible fluids with shear dependent viscosities, (2008), Technical Report 4/2008, University of Freiburg, DOWNLOAD PREPRINT. Journal of Mathematical Fluid Mechanics, (2010), No.1, 101-132, (2010); DOI: 10.1007/s00021-008-0277-y (online seit: 28. September 2008).
[27] D. Cruz-Uribe, SFO, L. Diening, and A. Fiorenza: A new proof of the boundedness of maximal operators on variable Lebesgue spaces (2008), Bollettino della Unione Matematica Italiana, Boll. Unione Mat. Ital. (9) 2 (2009), no. 1. DOWNLOAD PREPRINT
[26] L. Diening, P. Hästö, S. Roudenko: Function spaces of variable smoothness and integrability, Journal of Functional Analysis, (2009), 256, no. 6, 1731-1768, arXiv preprint.
[25] L. Diening, P. Harjulehto, P. Hästö, Y. Mizuta, T. Shimomura: Maximal functions in variable exponent spaces: limiting cases of the exponent, (2009), Annales Academiae Scientiarum Fennicae, vol 34, 503-522.
[24] M. Ruzicka, L. Diening: Non-Newtonian fluids and function spaces, Nonlinear Analysis, Function Spaces and Applications}, Vol. 8 (2007), 95-143.
[23] L. Diening, Ch. Kreuzer: Linear convergence of an adaptive finite element method for the p-laplacian equation, SIAM J. Numer. Anal., 46 (2008), 614-638. DOWNLOAD PREPRINT
[22] L. Diening, J. Malek, M. Steinhauer: On Lipschitz Approximations of Sobolev functions (with variable exponent) and their selected applications, ESAIM: Control, Optimisation and Calculus of Variations, published online DOI: 10.1051/cocv:2007049. (2006). DOWNLOAD PREPRINT
[22] L. Diening, M. Ruzicka: Interpolation Operators in Orlicz-Sobolev Spaces, Numerische Mathematik, 107 (2007) no. 1, 107-129. (2006).
[20] L. Diening, S. Samko: Hardy-Inequality in variable exponent Lebesgue spaces. Fractional Calculus and Applied Analysis, 10 (2007), no. 1, 1-19.
[19] L. Diening, F. Ettwein: Fractional estimates for non-differentiable elliptic systems with general growth. Forum Mathematicum, (2008) no. 3, 523-556.
[18] L. Diening, C. Ebmeyer, M. Ruzicka: Optimal Convergence for the Implicit Space-Time Discretization of Parabolic Systems with p-Structure. SIAM J. Numer. Anal., 45 (2007), no. 2, 457-472.
[17] L. Diening P. Hästö: Further Results on Variable Exponent Trace Spaces. Proceedings of the ISAAC conference, Catania (2005).
[16] L. Diening (joint with P. Hästö): Traces of Sobolev Spaces with Variable Exponents, Oberwolfach Report 30/2005, 1714-1716. DOWNLOAD PREPRINT
[15] L. Diening, A. Prohl, M. Ruzicka: Semi implicit Euler scheme for generalized Newtonian fluids. SIAM J. Numer. Anal. 44 (2006), no. 3, 1172-1190.
[14] L. Diening, P. Hästö, A. Nekvinda. Open Problems in Variable Exponent Lebesgue and Sobolev Spaces, Proceedings, Function Spaces, Differential Operators and Nonlinear Analysis FSDONA 2004, Academy of Sciences of the Czech Republic, Prague, 38-52, (appeared 2005).
[13] L. Diening, P. Hästö. Variable Exponent Trace Spaces. Studia Math., no. 183, 127-141.
[12] L. Diening, F. Ettwein, M. Ruzicka: C1,α -regularity for electrorheological fluids in two dimensions, Nonl. Diff. Eq. and Appl., 14 (2007) no 1-2, 207-217.
[11] L. Diening and M. Ruzicka: Strong solutions for generalized Newtonian fluids. Journal of Mathematical Fluid Mechanics (2005) no. 3, 413-450.
[10] L. Diening: Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces. Preprint, Mathematische Fakultät, Albert-Ludwigs-Universität Freiburg (2003), Bulletin des Sciences Mathematiques 129, (2005) no. 8, 657-700.
[9] L. Diening and M. Ruzicka: Integral operators on the halfspace in generalized Lebesgue spaces Lp(.), part II, Journal of Mathematical Analysis and Applications, 298 (2): 572-588, (2004).
[8] L. Diening and M. Ruzicka: Integral operators on the halfspace in generalized Lebesgue spaces Lp(.), part I, Journal of Mathematical Analysis and Applications, 298 (2): 559-571 (2004).
[7] L. Diening, A. Prohl, and M. Ruzicka: On time-discretizations for generalized Newtonian fluids. In Birman, Michael Sh. (ed.) et al., Nonlinear problems in mathematical physics and related topics II. In honour of Professor O. A. Ladyzhenskaya. New York, NY: Kluwer Academic Publishers. Int. Math. Ser., N.Y. 2, 89-118 (2002).
[6] L. Diening. Riesz potential and Sobolev embeddings of generalized Lebesgue and Sobolev spaces Lp(.) and Wk,p(.). Mathematische Nachrichten, 268(1):31-43 (2004).
[5] L. Diening and M. Ruzicka. Calderon-Zygmund operators on generalized Lebesgue spaces Lp(.) and problems related to fluid dynamics. J. Reine Angew. Math., 563:197-220 (2003).
[4] L. Diening. Maximal function on generalized Lebesgue spaces Lp(.). Mathematical Inequalities and Applications, 7(2), 2004 (preprint 2002)
[3] L. Diening. Theoretical and numerical results for electrorheological fluids. PhD thesis, Univ. Freiburg im Breisgau, Mathematische Fakultät, 156 p. (2002). DOWNLOAD
[2] J. Hoefkens, L. Diening, M. Berz, and B. Erdelyi. The WebCOSY System for Course Management in Distance Education. Journal of Computers in Mathematics and Science Teaching, 20(3):307-321 (2001).
[1] B. Erdelyi, J. Hoefkens, L. Diening, K. Makino, and M. Berz. The Michigan State University M.Sc. and Ph.D. Online Degree Programs in Beam Physics. Quarterly Review of Distance Education, 1(4):345-350, 2000.