Gieri Simonett
Professor
Department of Mathematics
Vanderbilt University
Nashville, TN 37240
Office: Stevenson Center 1523
Phone: (615) 322-6658 or 322-6672
Fax: (615) 343-0215
Email: gieri.simonett "at" vanderbilt.edu
i
Lara and Oriana
Teaching
Research Interests
-
Nonlinear Partial Differential Equations
-
Geometric Evolution Equations
- Free Boundary Problems
- Phase Transitions
- Fluid Dynamics
- Theory of Function Spaces
Books
Topics in nonlinear analysis. The Herbert Amann anniversary volume.
Edited by Joachim Escher and Gieri Simonett.
Progress in Nonlinear Differential Equations and their
Applications, 35.
Birkhäuser Verlag, Basel, 1999.
www.birkhauser.com
Mathematical models in medical and health science.
Papers from the International Conference held at
Vanderbilt University,
Nashville, TN, May 28--31, 1997.
Edited by Mary Ann Horn, Gieri Simonett and Glenn F. Webb.
Innovations in Applied Mathematics. Vanderbilt University Press,
Nashville, TN, 1998.
www.vanderbilt.edu/vupress
Recent Publications
Joachim Escher, Gieri Simonett
Maximal regularity for a free boundary problem.
NoDEA Nonlinear Differential Equations Appl. 2
(1995), no. 4, 463-510.
(pdf file).
Gieri Simonett,
Center manifolds for quasilinear reaction-diffusion systems.
Differential Integral Equations 8
(1995), no. 4, 753-796.
(ps file).
Joachim Escher, Gieri Simonett
Analyticity of the interface in a free boundary problem.
Math. Ann. 305
(1996), no. 3, 439-459.
(pdf or
ps file).
Joachim Escher, Gieri Simonett,
On Hele-Shaw models with surface tension.
Math. Res. Lett. 3 (1996), no. 4,
467-474.
(pdf or
ps file).
Xuan T. Duong, Gieri Simonett,
$H_\infty$-calculus for elliptic operators with non-smooth coefficients.
Differential Integral Equations 10
(1997), 201-217.
(pdf or
ps file).
Joachim Escher, Gieri Simonett,
Classical solutions of multi-dimensional Hele-Shaw models.
SIAM J. Math. Anal. 28 (1997), 1028-1047.
(pdf or
ps file).
Joachim Escher, Gieri Simonett,
Classical solutions for Hele-Shaw models with surface tension.
Adv. Differential Equations 2 (1997),
619-642.
(pdf or
ps file).
Joachim Escher, Gieri Simonett
Classical solutions for the quasi-stationary Stefan problem
with surface tension.
Differential Equations, Asymptotic
Analysis, and Mathematical Physics
(M. Demuth and B.-W. Schulze,
eds.),
Mathematical Research Vol. 100, Akademie Verlag, Berlin (1997),
619-642.
(pdf or
ps file).
Joachim Escher, Gieri Simonett,
A center manifold analysis for the Mullins-Sekerka model.
J. Differential Equations 143
(1998), 267-292.
(pdf
file).
Joachim Escher, Gieri Simonett,
The volume preserving mean curvature flow near spheres.
Proc. Amer. Math. Soc. 126
(1998), 2789-2796.
(pdf or
ps file).
Joachim Escher, Uwe Mayer, Gieri Simonett,
The surface diffusion flow for immersed hypersurfaces.
SIAM J. Math. Anal. 29
(1998), 1419-1433.
(pdf file).
Joachim Escher, Uwe Mayer, Gieri Simonett,
On the surface diffusion flow.
Proc. Intern. Conf. on Navier-Stokes Equations
and Related Problems,
TEV/VSP, Vilnius/Utrecht (1998), 69-80.
(pdf or
ps file).
Joachim Escher, G. Simonett,
Moving surfaces and abstract parabolic evolution equations.
Topics in Nonlinear Analysis. The Herbert Amann
Anniversary Volume,
Birkhäuser, Basel (1999), 183-212.
(pdf or
ps file).
Uwe Mayer, Gieri Simonett,
Classical solutions for diffusion-induced grain-boundary motion.
Journal Math. Anal. Appl.
234 (1999), 660-674.
(pdf file).
Uwe Mayer, Gieri Simonett,
On diffusion-induced grain-boundary motion.
Nonlinear Partial Differential Equations
(G.Q. Chen and E. DiBenedetto, eds.),
Contemporary Mathematics 238,
AMS, Providence (1999), 231-240.
(pdf or
ps file).
Uwe Mayer, Gieri Simonett,
Self-intersections for the surface diffusion
and the the
volume preserving mean curvature flow.
Differential Integral Equations
13 (2000), 1189-1199.
(pdf or
ps file).
G. Simonett,
The Willmore flow near spheres.
Differential Integral Equations
14 (2001),1005-1014.
(pdf or
ps file).
Philippe Clement, Gieri Simonett,
Maximal regularity in continuous interpolation spaces
and quasilinear parabolic equations.
J. Evolution Equations
1 (2001), 39-67.
(pdf file).
Uwe F. Mayer, Gieri Simonett,
A numerical scheme for axisymmetric solutions
of curvature driven
free boundary problems,
with applications to the Willmore flow.
Interfaces and Free Boundaries
4 (2002),1-22.
(pdf or
ps file).
Numerical simulations
Joachim Escher, Jan Prüss, Gieri Simonett,
On the Stefan problem with surface tension.
Elliptic and Parabolic Problems,
Proceedings of the 4th European Conference.
World Scientifici Publishing, New Jersey (2002), 377--388.
(pdf or
ps file).
Uwe F. Mayer, Gieri Simonett,
Self-intersections for the Willmore flow.
Evolution Equations: Applications to Physics, Industry, Life Sciences
and Economics.
EVEQ 2000 Conference in Levico Terme (Trento, Italy).
Birkhauser, Basel (2003), 341--348.
(pdf or
ps file).
Joachim Escher, Jan Prüss, Gieri Simonett,
A new approach to the regularity of solutions for
parabolic equations.
Evolution Equations: Proceedings in Honor of J.A. Goldstein's
60th Birthday,
Marcel Dekker, New York (2003), 167--190.
(pdf or
ps file).
Joachim Escher, Jan Prüss, Gieri Simonett,
Analytic solutions for a Stefan problem with
Gibbs-Thomson correction.
J. Reine Angew. Math. 563
(2003), 1--52.
(pdf file).
Joachim Escher, Gieri Simonett,
Analyticity of solutions to fully nonlinear
parabolic evolution equations
on symmetric spaces.
J. Evolution Equations 3
(2003), 549--576.
(pdf or
ps file).
Philippe Clement, Stig-Olof Londen, Gieri Simonett,
Quasilinear evolutionary equations and continuous
interpolation spaces.
J. Differential Equations 196
(2004), 418--447.
(pdf file).
Jan Prüss, Gieri Simonett,
Maximal regularity for evolution equations in weighted L_p spaces.
Arch. Math. 82 (2004), 415--431.
(pdf file).
Dieter Bothe, Jan Prüss, Gieri Simonett,
Well-posedness of a two-phase flow with soluble surfactant.
In: Nonlinear Elliptic and Parabolic Problems. A Special Tribute to the Work of
Herbert Amann.
Progress in Nonlinear Differential Equations and Their Applications, Vol. 64,
Birkhäuser, Basel (2005), 37--62.
(pdf file).
Gieri Simonett, Christoph Walker,
On the solvability of a mathematical model for prion proliferation.
J. Math. Anal. Appl. 324 (2006), 580--603.
(pdf file).
Jan Prüss, Gieri Simonett,
Operator-valued symbols for elliptic and
parabolic problems on wedges.
Partial Differential Equations and Functional Analysis
The Philippe Clément Festschrit.
Operator Theory: Advances and Applications, Vol. 168,
Birkhäuser, Basel (2006), 189--208.
(pdf file).
Jan Prüss, Gieri Simonett,
$H^\infty$-calculus for the sum of non-commuting operators.
Trans. Amer. Math. Soc. 359 (2007), 3549-3565.
(pdf file).
Jan Prüss, Jürgen Saal, Gieri Simonett,
Existence of analytic solutions for
the classical Stefan problem.
Math. Ann. 338 (2007), 703-755.
(pdf file).
Jan Prüss, Jürgen Saal, Gieri Simonett,
Analytic solutions for the classical two-phase Stefan problem.
Proceedings of Equadiff-11, (2007), 415--425.
(pdf file).
Jan Prüss, Gieri Simonett,
Maximal regularity for degenerate evolution equations with an exponential
weight function.
Functional Analysis and Evolution Equations. Dedicated to Gunter Lumer.
Birkhäuser, Basel (2007), 531--546.
(pdf file).
Jan Prüss, Gieri Simonett,
Stability of equilibria for the Stefan problem with surface tension.
SIAM J. Math. Anal. To appear.
(pdf file).
Jan Prüss, Gieri Simonett,
Regularity for the Navier-Stokes equations
with
surface tension on the free boundary.
In preparation.