Veröffentlichungen von Reiner Schätzle


  1. Elliott, C.M., Paolini, M., Schätzle, R.:
    Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow,
    Mathematical Models and Methods in Applied Sciences , (1996), 6, No. 8, pp. 1103--1118.
  2. Elliott, C.M., Schätzle, R.:
    The limit of the anisotropic double-obstacle Allen-Cahn equation,
    Proceedings of the Royal Society of Edinburgh, (1996), 126 A, pp. 1217--1234.
  3. Elliott, C.M., Schätzle, R.:
    The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the non-smooth case,
    SIAM Journal on Mathematical Analysis, (1997), Vol. 28, No. 2, pp. 274--303.
  4. Schätzle, R.:
    A counterexample for an approximation of the Gibbs-Thomson law,
    Advances in Mathematical Sciences and Applications, (1997), Vol. 7, No. 1, pp. 25--36.
  5. Canarius, T., Schätzle, R.:
    Finiteness and positivity results for global minimizers of a semilinear elliptic problem,
    Journal of Differential Equations, (1998), 148, pp. 212--229.
  6. Elliott, C.M., Gardiner, A., Schätzle, R.:
    Crystalline curvature flow in a variational setting,
    Advances in Mathematical Sciences and Applications, (1998), Vol. 8, No. 1, pp. 455--490.
  7. Elliott, C.M., Schätzle, R., Stoth, B.:
    Viscosity solutions of a degenerate parabolic elliptic system arising in the mean field theory of superconductivity,
    Archive of Rational Mechanics and Analysis, (1998), 145, pp. 99--127.
  8. Kratz, W., Liebscher, D., Schätzle, R.:
    On the definiteness of quadratic functionals,
    Annali di Matematica Pura ed Applicata, (1999), IV, Vol. CLXXVI, pp. 133--143.
  9. Nakamura, K.I., Matano, H., Hilhorst, D., Schätzle, R.:
    Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term,
    Journal of Statistical Physics, (1999), Vol. 95, No. 5/6, pp. 1165--1185.
  10. Schätzle, R., Stoth, B.:
    The stationary mean field model of superconductivity: Partial regularity of the free boundary,
    Journal of Differential Equations, (1999), 157, pp. 319--328.
  11. Schätzle, R., Styles, V.:
    Analysis of a Mean Field Model of Superconducting Vortices,
    European Journal of Applied Mathematics, (1999), 10, pp. 319--352.
  12. Henry, M., Hilhorst, D., Schätzle, R.:
    Convergence to a viscosity solution for an advection-reaction-diffusion equation arising from a chemotaxis-growth model,
    Hiroshima Mathematical Journal, (2000), Vol. 29, No. 3, pp. 591--630.
  13. Hilhorst, D., Logak, E., Schätzle, R.:
    Global existence for a nonlocal mean curvature flow as a limit of a parabolic-elliptic phase transition model,
    Interfaces and Free Boundaries, (2000), 2, pp. 267 -- 282.
  14. Schätzle, R.:
    On the perturbation of the zeros of complex polynomials,
    IMA Journal of Numerical Analysis, (2000), 20, pp. 185--202.
  15. Schätzle, R.:
    The quasi-stationary phase field equations with Neumann boundary conditions,
    Journal of Differential Equations, (2000), 162, No. 2, 473--503.
  16. Canarius, T., Schätzle, R.:
    Multiple solutions for a semilinear elliptic problem,
    Nonlinear Analysis TMA, (2001), Ser. A: Theory Methods, 45, No. 7, pp. 937--956.
  17. Hug, D., Schätzle, R.:
    Intersections and translative integral formulas for boundaries of convex bodies,
    Mathematische Nachrichten, (2001), 226, pp. 99--128.
  18. Kuwert, E., Schätzle, R.:
    The Willmore Flow with small initial energy,
    Journal of Differential Geometry, (2001), 57, No. 3, pp. 409--441.
  19. Schätzle, R.:
    Hypersurfaces with mean curvature given an ambient Sobolev function,
    Journal of Differential Geometry, (2001), 58, No. 3, pp. 371--420.
  20. Dziuk, G., Kuwert, E., Schätzle, R.:
    Evolution of Elastic Curves in $\rel^n$: Existence and Computation,
    SIAM Journal on Mathematical Analysis, (2002), 33, No. 5, pp. 1228--1245.
  21. Hilhorst, D., Peletier, L.A., Schätzle, R.:
    $\Gamma-$limit for the Extended Fisher-Kolmogorov equation,
    Proceedings of the Royal Society of Edinburgh, (2002), 132 A, pp. 141--162.
  22. Hug, D., Mani-Levitska, P., Schätzle, R.:
    Almost transversal intersections of convex surfaces and translative integral formulae,
    Mathematische Nachrichten, (2002), 246-247, pp. 121--155.
  23. Kuwert, E., Schätzle, R.:
    Gradient flow for the Willmore functional,
    Communications in Analysis and Geometry, (2002), 10, No. 2, pp. 307--339.
  24. Hilhorst, D., Mimura, M., Schätzle, R.:
    Vanishing latent heat limit in a Stefan-like problem arising in biology,
    Journal of Nonlinear Analysis: Series B Real World Applications, (2003), 4, pp. 261--285.
  25. Kuwert, E., Schätzle, R.:
    Removability of point singularities of Willmore surfaces,
    Annals of Mathematics, (2004), 160, No. 1, pp. 315--357.
  26. Schätzle, R.:
    Quadratic tilt-excess decay and strong maximum principle for varifolds,
    Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, (2004), Serie 5, Vol. III, pp. 171--231.
  27. Giga, Y., Ohtsuka, T., Schätzle, R.:
    On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations,
    Interfaces and Free Boundaries, (2006), 8, pp. 317--348.
  28. Röger, M., Schätzle, R.:
    On a modified conjecture of De Giorgi,
    Mathematische Zeitschrift, (2006), 254, no. 4, pp. 675--714.
  29. Kuwert, E., Schätzle, R.:
    Branch points for Willmore surfaces,
    Duke Mathematical Journal, (2007), 138, No. 2, pp. 179--201.
  30. Alfaro, M., Garcke, H., Hilhorst, D., Matano, H., Schätzle, R.:
    Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation,
    Proceedings of the Royal Society of Edinburgh, (2009), 140 A, no. 4, 673--706.
  31. Chill, R., Fasangova, E., Schätzle, R.:
    Willmore blow ups are never compact,
    Duke Mathematical Journal, (2009), 147, no. 2, pp. 345--376.
  32. Schätzle, R.:
    Lower semicontinuity of the Willmore functional for currents,
    Journal of Differential Geometry, (2009), 81, pp. 437--456.
  33. Banas, L., Prohl, A., Schätzle, R.:
    Approximation of heat flow and wave map to spheres varying in space and time,
    Numerische Mathematik, (2010), 115, no. 3, pp. 395--432.
  34. Kuwert, E., Li, Y., Schätzle, R.:
    The large genus limit of the infimum of the Willmore energy,
    American Journal of Mathematics, (2010), 132, No. 1, pp. 37--51.
  35. Schätzle, R.:
    The Willmore boundary problem,
    Calculus of Variations and Partial Differential Equations, (2010), 37, pp. 275--302.
  36. Kuwert, E., Schätzle, R.:
    Closed surfaces with bounds on their Willmore energy,
    Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, (2012), Serie 5, 11, pp. 605--634.
  37. Ndiaye, C.B., Schätzle, R.M.:
    A convergence theorem for immersions with $L^2$-bounded second fundamental form,
    Rendiconti del Seminario Matematico della Universita di Padova, (2012), 127, pp. 235--247.
  38. Röger, M., Schätzle, R.:
    Control of the isoperimetric deficit by the Willmore deficit,
    Analysis, (2012), 32, pp. 1--7.
  39. Kuwert, E., Schätzle, R.:
    Minimizers of the Willmore functional under fixed conformal class,
    Journal of Differential Geometry, (2013), 93, pp. 471--530.
  40. Schätzle, R.M.:
    Conformally constrained Willmore immersions,
    Advances in Calculus of Variations, (2013), 6, pp. 375--390.
  41. Schätzle, R.M.:
    Estimation of the conformal factor under bounded Willmore energy,
    Mathematische Zeitschrift, (2013), 274, pp. 1341--1383.
  42. Arendt, W., Schätzle, R.M.:
    Semigroups generated by elliptic operators in non-divergence form on $C_0(\Omega)$,
    Annali della Scuola Normale Superiore di Pisa, (2014), Serie 5, Vol. XIII, pp. 417--434.
  43. Lamm, T., Schätzle, R.M.:
    Optimal rigidity estimates for nearly umbilical surfaces in arbitrary codimension,
    Geometric and Functional Analysis, (2014), 24, no. 6, pp. 2029--2062.
  44. Ndiaye, C.B., Schätzle, R.M.:
    Explicit conformally constrained Willmore minimizers in arbitrary codimension,
    Calculus of Variations and Partial Differential Equations, (2014), 51, no. 1-2, pp. 291--314.
  45. Lamm, T., Schätzle, R.M.:
    Rigidity and non-rigidity results for conformal immersions,
    Advances in Mathematics, (2015), 281, pp. 1178--1201.
  46. Ndiaye, C.B., Schätzle, R.M.:
    Willmore surfaces with nonremovable singularities and number of critical levels,
    Mathematische Annalen, (2015), 312, 3, pp. 1201--1221.
  47. Ndiaye, C.B., Schätzle, R.M.:
    New examples of conformally constrained Willmore minimizers of explicit type,
    Advances in Calculus of Variations, (2015), 8, no. 4, pp. 291--319.
  48. Lamm, T., Schätzle, R.M.:
    Conformal Willmore Tori in $\rel^4$,
    Journal für die Reine und Angewandte Mathematik, (2018), 742, pp. 281--301.
  49. Eichmann, S., Schätzle, R.M.:
    Positivity for the clamped plate equation under high tension,
    Annali di Matematica Pura ed Applicata, (2022), 201, no. 4, pp. 2001--2020.
  50. Dall'Acqua, A., Müller, M., Schätzle, R.M., Spener, A.:
    The Willmore flow of tori of revolution,
    to appear in Analysis \& PDE, 2023.

Preprints


  1. Schätzle, R.M.:
    The umbilic set of Willmore surfaces,
    arXiv:math.DG/1710.06127, 2017.
  2. Eichmann, S., Schätzle, R.M.:
    The rotational symmetric Willmore boundary problem,
    preprint, 2024. (pdf-file)


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Reiner Schätzle, Universität Tübingen. (e-mail: schaetz at everest.mathematik.uni-tuebingen.de)