Veröffentlichungen von Reiner Schätzle
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Schätzle, R., Styles, V.:
Analysis of a Mean Field Model of Superconducting Vortices,
European Journal of Applied Mathematics, (1999),
10, pp. 319--352.
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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.
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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.
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Schätzle, R.:
On the perturbation of the zeros of
complex polynomials,
IMA Journal of Numerical Analysis, (2000),
20, pp. 185--202.
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Schätzle, R.:
The quasi-stationary phase field equations with
Neumann boundary conditions,
Journal of Differential Equations, (2000),
162, No. 2, 473--503.
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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.
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Hug, D., Schätzle, R.:
Intersections and translative integral formulas
for boundaries of convex bodies,
Mathematische Nachrichten, (2001),
226, pp. 99--128.
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Kuwert, E., Schätzle, R.:
The Willmore Flow with small initial energy,
Journal of Differential Geometry, (2001),
57, No. 3, pp. 409--441.
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Schätzle, R.:
Hypersurfaces with mean curvature
given an ambient Sobolev function,
Journal of Differential Geometry, (2001),
58, No. 3, pp. 371--420.
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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.
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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.
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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.
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Kuwert, E., Schätzle, R.:
Gradient flow for the Willmore functional,
Communications in Analysis and Geometry, (2002),
10, No. 2, pp. 307--339.
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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.
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Kuwert, E., Schätzle, R.:
Removability of point singularities of Willmore surfaces,
Annals of Mathematics, (2004),
160, No. 1, pp. 315--357.
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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.
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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.
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Röger, M., Schätzle, R.:
On a modified conjecture of De Giorgi,
Mathematische Zeitschrift, (2006),
254, no. 4, pp. 675--714.
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Kuwert, E., Schätzle, R.:
Branch points for Willmore surfaces,
Duke Mathematical Journal, (2007),
138, No. 2, pp. 179--201.
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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.
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Chill, R., Fasangova, E., Schätzle, R.:
Willmore blow ups are never compact,
Duke Mathematical Journal, (2009),
147, no. 2, pp. 345--376.
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Schätzle, R.:
Lower semicontinuity of the Willmore functional
for currents,
Journal of Differential Geometry, (2009),
81, pp. 437--456.
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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.
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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.
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Schätzle, R.:
The Willmore boundary problem,
Calculus of Variations
and Partial Differential Equations, (2010),
37, pp. 275--302.
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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.
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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.
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Röger, M., Schätzle, R.:
Control of the isoperimetric deficit by the Willmore deficit,
Analysis, (2012),
32, pp. 1--7.
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Kuwert, E., Schätzle, R.:
Minimizers of the Willmore functional
under fixed conformal class,
Journal of Differential Geometry, (2013),
93, pp. 471--530.
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Schätzle, R.M.:
Conformally constrained Willmore immersions,
Advances in Calculus of Variations, (2013),
6, pp. 375--390.
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Schätzle, R.M.:
Estimation of the conformal factor
under bounded Willmore energy,
Mathematische Zeitschrift, (2013),
274, pp. 1341--1383.
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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.
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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.
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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.
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Lamm, T., Schätzle, R.M.:
Rigidity and non-rigidity results for conformal immersions,
Advances in Mathematics, (2015),
281, pp. 1178--1201.
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Ndiaye, C.B., Schätzle, R.M.:
Willmore surfaces with nonremovable singularities
and number of critical levels,
Mathematische Annalen, (2015),
312, 3, pp. 1201--1221.
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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.
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Lamm, T., Schätzle, R.M.:
Conformal Willmore Tori in $\rel^4$,
Journal für die Reine und Angewandte Mathematik, (2018),
742, pp. 281--301.
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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.
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Dall'Acqua, A., Müller, M., Schätzle, R.M., Spener, A.:
The Willmore flow of tori of revolution,
to appear in Analysis \& PDE, 2023.
Preprints
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Schätzle, R.M.:
The umbilic set of Willmore surfaces,
arXiv:math.DG/1710.06127, 2017.
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Dall'Acqua, A., Schätzle, R.M.:
Rotational symmetric Willmore surfaces with umbilic lines,
preprint, 2024. (pdf-file)
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Eichmann, S., Schätzle, R.M.:
The rotational symmetric Willmore boundary problem,
preprint, 2024. (pdf-file)
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Homepage.
Reiner Schätzle, Universität Tübingen.
(e-mail: schaetz at everest.mathematik.uni-tuebingen.de)