Prof. Dr. Stephan Luckhaus

	Profilbildender Forschungsbereich "Mathematical Sciences"
	Forschungsinteressen
	Lebenslauf
	Aktuelle Projekte
	Publikationen
	Kontakt

Profilbildender Forschungsbereich "Mathematical Sciences"

Forschungsinteressen

• Harmonische Abbildungen
  Hauptresultat ist ein Interpolationslemma für Randwerte (Art. [11], [17])
• Elliptisch parabolische Systeme
  Hauptresultat sind die Existenzsätze in dem gemeinsamen Artikel (Art.[2] mit H. W. Alt)
• Fluss im porösen Medium (Art. [4], [5], [21], [22], [23], [24])
• Homogenisierung (Artikel [22], [25])
• Phasenübergänge
  Hauptresultate sind das Existenzresultat für Systeme von Stefanproblemen bei Mehrkomponentendiffusion mit A. Visintin (Art. [3])  und die globale Lösung für das Gibbs Thomson Problem (Art. [13]

• freie Randwertprobleme im Allgemeinen
• Mathematische Bildverarbeitung und
• neuerdings im Zusammenhang mit Phasenübergängen Vielteilchensysteme

Lebenslauf

Aktuelle Projekte

• Mathematische Modellierung von Diffusionsinduzierter Segregation
• Ein Mathematisches Modell für Phasen-Übergänge in Kristallen

Publikationen

Artikel

1. S. Luckhaus:
   Existence and regularity of weak solutions for the Dirichlet problem for semilinear elliptic systems of higher order.
   J. Reine Ang. Math. 306 (1979), 192-207 
2. H. W. Alt, S. Luckhaus:
   Quasilinear elliptic-parabolic differential equations .
   Math. Z. 183 (1983), 311-341 
3. S. Luckhaus, A. Visintin:
   Phase transitions in multicomponent mixtures.
   Man. mat. 43 (1983), 261-288 
4. H. W. Alt, S. Luckhaus, A. Visintin:
   On nonstationary flow through porous media.
   Annali Mat. Pura ed Appl. 136 (1984), 306-316
5. D. Kröner, S. Luckhaus:
   Flow of oil and water in a porous medium.
   JDE 55 (1984), 276-288
6. G. Anzellotti, S. Luckhaus:
   Dynamical evolution of elasto-perfectly plastic bodies.
   App. Math. Opt. 15 (1987), 121-140 
7. W. Härdle, S. Luckhaus:
   Uniform consistency for a class of regression function estimators.
   Ann. Stat. 12 (1984), 612-623
8. S. Luckhaus:
   Global boundedness for a delay differential equation.
   Trans. AMS 294 (1986), 767-774 
9. R. Dal Passo, S. Luckhaus:
   On a degenerate diffusion equation not in divergence form.
   JDE 69 (1987), 1-14
10. S. Luckhaus, U. Thiel:
    A Stefan problem in combustion.
    Acta Appl. Mat. 9 (1987), 199-217 
11. S. Luckhaus:
    Partial Hölder continuity for minima of certain energies among maps into a Riemannian manifold.
    Indiana U. Math. J. 37 (1988), 349-367 
12. S. Luckhaus, L. Modica:
    The Gibbs Thompson relation within the gradient theory of phase transitions.
    ARMA 107 (1989), 71-89 
13. S. Luckhaus:
    Solutions for the two phase Stefan problem with the Gibbs Thompson law for the melting temperature.
    EJAM 1 (1990), 101-112 
14. H. Engler, B. Kawohl, S. Luckhaus:
    Gradient estimates for solutions of parabolic equations and systems.
    J. Math. An. and Appl. 147 (1990), 309-329
15. S. Luckhaus, W. Sauermann:
    Multinomial approximations for nonparametric experiments which minimize the maximal loss of Fisher information .
    J. Prob. Rel. Fields 81 (1991), 159-184
16. W. Jäger, S. Luckhaus:
    Blow up for a reaction diffusion system.
    Trans AMS 329 (1992), 819-824
17. S. Luckhaus:
    Convergence of minimizers for the p- Dirichlet integral.
    Math. Z. 213 (1993), 449-456 
18. J. Filo, S. Luckhaus:
    Asymptotic expansion for a periodic boundary condition
    JDE 120 (1995), 133-173 
19. S. Luckhaus, S. Zheng:
    A nonlinear boundary value problem involving a nonlocal term.
    JNA TMA 22(1994), 129-135 
20. S. Luckhaus, T. Sturzenhecker:
    Implicite time discretization for the mean curvature flow equation.
    Calc. Var. 3 (1995), 253-271 
21. G. Gilardi, S. Luckhaus:
    A regularity result for the solution to the dam problem.
    JNA TMA 26 (1996), 113-138 
22. G. Gilardi, S. Luckhaus:
    Extension of a regularity result concerning the dam problem.
    Rend. Mat. Acc. Lincei, s. 9, 2 (1991) 4, 287-296
23. A. Bourgeat, S. Luckhaus, A. Mikelic:
    Convergence of the homogenization process for a double porosity model of immiscible two phase flow.
    SIAM J. Math An. 27 (1996) , 1520-1543 
24. J. Filo, S. Luckhaus:
    Modelling surface runoff and infiltration of rain by an elliptic-parabolic equation coupled with a first order equation on the boundary.
    ARMA 146 (1999) 2, 157-182 
25. S. Luckhaus, P. Plotnikov:
    Entropy solutions to a Buckley Leverett equation .
    Sib. J. Math. 41 (2000)  2, 329-348 
26. J. Filo, S. Luckhaus:
    Homogenization for a boundary condition for the heat equation.
    JEMS 2 (2000) 3, 217-258
27. N. Dirr, S. Luckhaus:
    Mesoscopic limit for nonisothermal phase transitions .
    Markov Processes 7 (2001) 3, 355-382
28. S. Luckhaus, J. Malek:
    On an evolutionary nonlinear fluid model in the limiting case.
    Math. Boh. 126 (2001) 2, 421-428
29. N. Dirr, S. Luckhaus, M. Novaga:
    A stochastic selection principle in case of fattening for mean curvature flow.
    Calc Var 13 (2001), 405-425
30. T. Blesgen, S. Luckhaus, K. Bente:
    Modelling and numerical simulation of diffusion induced segregation.
    Chryst. Res. Technol. 37 (2002)6, 570-580
31. S. Luckhaus, L. Triolo:
    A continuum reaction diffusion limit of a stochastic cellular growth model.
    Rend. Acc. dei Lincei s. 9, 15 (2004), 215-223
32. T. Blesgen, S. Luckhaus, K. Bente:
    Diffusion induced segregation in the case of the ternary system sphalerite, chalcopyrite and cubanite.
    Cryst. Res. Technol. 39 (2004)11, 969-979
33. S. Luckhaus:
    Uniform rectifiability from mean curvature bounds.
    Rec. Adv. Ell. Parab. Probl. (2005), 199-202
34. T. Blesgen, S. Luckhaus:
    The dynamics of transition layers in solids with discontinous chemical potentials.
    Math. Meth. Appl. Sci. 29 (2006), 525-536
35. G. Belletini, M.S. Gelli, S. Luckhaus, M. Novaga:
    Deterministic equivalent for the Allen Cahn energy of a scaling law in the Ising model.
    Calc. Var. 26 (2006), 429-445
36. T. Blesgen, S. Luckhaus, L. Mugnai:
    Discrete free energy functionals for elastic material with phase change.
    Analysis, modeling and simulation of multiscale problems. Berlin: Springer 2006, 426-434.
37. S. Arnrich, T. Blesgen, S. Luckhaus:
    A general theory for elastic phase transitions in crystal.
    Analysis, modeling and simulation of multiscale problems. Berlin: Springer 2006, 179-196.
38. S. Luckhaus, Y. Sugiyama:
    Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems.
    M2AN Math. Model. Numer. Anal. 40 (2006)3, 597-621.
39. A. De Masi, S. Luckhaus, E. Presutti:
    Two scales hydrodynamic limit for a model of malignant tumor cells.
    Ann. IHP, Prob. and Stat. 43 (2007), 257-297.
40. S. Luckhaus, Y. Sugiyama:
    Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases.
    Math. J. Indiana Univ. 56 (2007), 1279-1297.
41. S. Luckhaus, L.S. Luboobi, J.Y.T. Mugisha, J. Tumwiine:
    An Age-structured mathematical model for the within host dynamics of malaria and the immune system.
    J. Math. Model Algor 7 (2008), 79-97.
42. S. Luckhaus:
    Uniform Rectifiability from Mean Curvature Bounds.
    Z. Anal. Anw. 27 (2008), 451-461.

Conference Proceedings

Reports, Preprints

1. S. Luckhaus:
   The Douglas problem for surfaces of prescribed mean curvature.
   Preprint 234, SFB 72, Bonn (1978)
2. S. Luckhaus:
   C ^1,ε,  -regularity for energy minimizing Holder continuous p-harmonic maps beetweeen Riemannian manifolds.
   Preprint CMA, Canberra (1986)
3. S. Luckhaus:
   Partial boundary regularity for the capillarity problem in arbitrary space dimension.
   Preprint 416, SFB 123, Heidelberg (1987)
4. H. Engler, S. Luckhaus:
   Weak solution classes for parabolic integrodifferential equations.
   MRC Report 2422, Madison
5. C. Elliott, S. Luckhaus:
   A generalized diffusion equation for phase separation of a multicomponent mixture with interfacial free energy .
   Preprint 887, IMA, Minneapolis
6. S. Luckhaus:
   The Stefan problem with the Gibbs Thompson law .
   Report Univ. Pisa 591(1991)
7. S. Luckhaus:
   Solidification of alloys and the Gibbs Thompson law.
   Preprint 335, SFB 256, Bonn
8. S. Luckhaus, K. Räwer, J. Rittscher:
   A new gamma-convergent approximation of the Mumford Shah functional.
   Preprint 517, SFB 256, Bonn
9. M. Kimura, S. Luckhaus:
   Avariational problem arising from the Mullins Sekerka Problem.
   Preprint MPI MIS (2001)
   

Kontakt

Sekretariat:

Abteilung:

Postadresse:

Prof. Dr. Stephan Luckhaus
Mathematisches Institut
Fakultät für Mathematik und Informatik
Universität Leipzig
04081 Leipzig

Besucheradresse:

Johannisgasse 26
04103 Leipzig