EDUCATION

1981           Diploma in Mathematics at Leipzig University

1986           Dissertation (Ph.D.) defended at Leipzig University

1998           Habilitation defended at Leipzig University

WORK EXPERIENCE

1981–1995 Teaching Assistant, Mathematics Department, Leipzig University

1995–1997 Habilitation Fellow, University of Cologne, with Prof. B. Kawohl

1999–2001 Postdoctoral Fellow, Mathematics Department, University of Missouri-Columbia

2001–2006 Assistant Professor at the University of Chile (Santiago)

2007  Visiting Associate Professor at the American University of Beirut (AUB), (Lebanon)

2008 -2012 Associate Professor at AUB

2012- 2015 Professor (W3) at Leipzig University

2015- 2017 Professor (W2) at University of Rostock

2017-          Professor at South China University of Technology

SCIENTIFIC VISITS 

1986–1987 Steklov Mathematical Institute of the USSR Academy of Sciences, St. Petersburg

1995           Mathematical Institute in Oberwolfach, with A.Yu. Solynin (St. Petersburg)

1997           University of Naples (Italy)

2010           University of Louvain (Belgium)

2010- 2011 Leipzig University (Germany)

2012           University of Naples

2015           University of Naples

2015           Universidad de Concepcion (Chile)

TEACHING EXPERIENCE

1981-1995   Teaching Assistant at Leipzig University.

since 1995 lecturer at several universities in Germany and abroad, for undergraduate and graduate students in Mathematics, Engineering and other Sciences

Courses: Calculus I-III, Linear Algebra, Complex Analysis, ODE, PDE, Functional Analysis, Calculus of Variations and other subjects.

RESEARCH INTERESTS 

1981–1986 Nonlinear functional analysis with applications to mechanics of continua: existence and regularity of solutions of axially symmetric cavity problems.

1987–     geometric properties of solutions to elliptic and parabolic differential equations, isoperimetric inequalities.

2004 –        existence, multiplicity and regularity of solutions to singular elliptic problems.

Methods: symmetrization, continuous rearrangement, maximum principles, principle of unique continuation, blow-up techniques, topological degree methods.

PUBLICATIONS

1. Axially symmetric flows with finite cavities, Zeitschr. Anal. Anw., 12 (1993), I: 97–112, II: 297–303.

2. Steiner symmetrization and periodic boundary value problems, Zeitschr. Anal. Anw. 13 (1995), 417–423.

3. A reverse convolution-inequality, J. Convex Anal. 1 (1994), 259–264.

4. Continuous Steiner symmetrization, Math. Nachr. 172 (1995), 25–48.

5. Continuous polarization and symmetry of solutions of variational problems with potentials, Calculus of variations, applications and computations (Pont–Mousson, 1994), 25–34, Pitman Res. Notes Math. Ser. 326, Longman Sci. Tech., Harlow, 1995.

6. An approach to symmetrization via polarization, (with A.Yu. Solynin), Trans. Amer. Math. Soc. 352 (2000), no. 4, 1759–1796.

7. A symmetry problem in the calculus of variations, (together with V. Ferone and B. Kawohl), Calc. Var. 4 (1996), 593–596.

8. Weighted Dirichlet-type inequalities for Steiner symmetrization, Calc. Var. 8 (1999), 15–25.

9. Radial symmetry for nonnegative solutions of semilinear elliptic problems involving the p-Laplacian, Progress in partial differential equations, Vol.1 (Pont–Mousson, 1997), 46–57, Pitman Res. Notes Math. Ser. 383, Longman, Harlow, 1998.

10. One-dimensionality of solutions of semilinear elliptic problems in cylindrical domains, ZAMM Z. Angew. Math. Mech. 80 (2000), no. 5, 345–350.

11. An elementary proof for one-dimensionality of traveling waves in cylinders, J. Inequal. Appl. 4 (1999), no. 3, 265–281.

12. A weighted isoperimetric inequality and applications to symmetrization, (with F. Betta, A. Mercaldo and M.R. Posteraro), J. Inequal. Appl. 4 (1999), no. 3, 215–240,

13. Continuous rearrangement and symmetry of solutions of elliptic problems, Proc. Indian Acad. Sci. Math. Sci. 110 (2000), no. 2, 157–204.

14. Some new symmetry results for elliptic problems on the sphere and in Euclidean space, (with J. Prajapat), Rend. Circ. Mat. Palermo (2) 49 (2000), no. 3, 445–462.

15. A general rearrangement inequality ´a la Hardy-Littlewood, J. Inequal. Appl. 5 (2000), no. 4, 309–320.

16. An isoperimetric inequality for eigenvalues of the Stekloff problem, ZAMM Z. Angew. Math. Mech. 81 (2001), no. 1, 69–71.

17. A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative. (with A. Henrot), Rend. Circ. Mat. Palermo (2) 51 (2002), no. 3, 375–390.

18. A comparison result related to Gauss measure. (with M.F. Betta, A. Mercaldo, M.R. Posteraro), C. R. Math. Acad. Sci. Paris 334 (2002), no. 6, 451–456.

19. Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli. Electr. Journ. of Differ. Equations 108 (2003), 1–20.

20. Positivity and radial symmetry of solutions to some variational problems in R N . J. Math. Anal. Appl. 296 (2004), no.1, 226–243.

21. Semilinear singular elliptic equations with dependence on the gradient. (with L. Iturriaga, P. Ubilla), Nonlinear Analysis 65, no.3, (2006), 601–614.

22. Existence of positive solutions for p-Laplacian problems with weights. (with L. Iturriaga, J. Sanchez, P. Ubilla), Commun. Pure Appl. Analysis 5, no.4, (2006), 941–952.

23. An isoperimetric inequality related to Gaussian measure and applications. (with F. Chiacchio, A. Mercaldo), Matematiche (Catania) 60 (2005), no. 2, 419–423 (2006).

24. Weighted isoperimetric inequalities on Rⁿ and applications to rearrangements. (with M.F. Betta, A. Mercaldo, M.R. Posteraro), Math. Nachrichten 281 (2008), no.4, 466–498.

25. On the Rayleigh quotient and the first eigenvalue for some vector-valued variational problems. (with R. Manasevich), Differ. Integral Equations 20 (2007), no.4, 429–443.

26. Rearrangements and Applications to Symmetry Problems in PDE. in: Handbook of Differential Equations, vol.4: Stationary Partial Differential Equations, Birkh¨auser 2007, 58 pp.

27. Asymptotic estimates at infinity for p-Laplace equations in exterior domains (with A. Avila), Nonlinear Anal. 69 (2008), 1615-1628.

28. A multiplicity result for the p−-Laplacian involving a parameter. (with L. Iturriaga, P. Ubilla). Ann. Henri Poincare 9 (2008), no. 7, 1371–1386.

29. A class of degenerate elliptic equations and a Dido’s problem with respect to a measure. (with F. Chiacchio, A. Mercaldo.) J. Math. Anal. Appl. 348 (2008), no. 1, 356–365.

30. Best constants for Hardy-type inequalities in a half–space. 6 pp., Proceedings of a conference in Analysis and Computational Mathematics, NDU, Beirut 2008.

31. On weighted symmetrization w.r.t. infinite measures and applications to PDE. (with A. Mercaldo, M.R. Posteraro). Rev. Mat. Iberoam. 29 (2013), no. 2, 665–690.

32. A relative isoperimetric inequality. (with M. Willem). Commun. Contemp. Math. 14 (2012), no.3, 1250023, 6 pp.

33. Weighted isoperimetric inequalities in cones and applications. (with F. Chiacchio, A. Mercaldo). Nonlinear Anal. 75 (2012), no.15, 5737-5755.

34. A weighted isoperimetric inequality in an orthant. (with F. Chiacchio, A. Mercaldo). Potential Anal. 41 (2014), no. 1, 171-186.

35. Optimal Szeg¨o-Weinberger type inequalities. (with F. Chiacchio, G. di Blasio). Commun. on Pure Appl. Analysis 15 (2016), no.2, 367–383.

36. Convergence of two-dimensional staggered central schemes on unstructured triangular grids. (with G. Jannoun, R. Touma). Appl. Numer. Math. 92 (2015), 1-20.

37. An isoperimetric inequality for Gauss-like product measures. (with F. Chiacchio, A. Mercaldo). J. Math. Pures Appl. (9) 106 (2016), no. 2, 375–391.

38. Symmetry for a general class of overdetermined elliptic problems. Nonlinear Differ. Equ. Appl. 23, no.3 (2016), 1–16. 39. Some isoperimetric inequalities on R N with respect to weights |x| α. (with A. Alvino, F. Chiacchio, A. Mercaldo, M.R. Posteraro). 40 pp. (2016), to appear in: J. Math. Anal. Appl. arXiv:1606.02195.

40. Symmetry and asymmetry of minimizers of a class of noncoercive functionals. (with G. Croce, O. Guibe, A. Mercaldo). to appear in: Adv. Calc. Var. (2017). arXiv:1601.07327. 

Submitted for publication:

41. New P´olya-Szeg¨o-type inequalities and an alternative approach to comparison results for PDE’s. (with F. Chiacchio, A. Ferone and A. Mercaldo). 18 pp.

42. On weighted isoperimetric inequalities with nonradial densities. (with A. Alvino, F. Chiacchio, A. Mercaldo, M.R. Posteraro). 12 pp. (2018). 

Work as editor:

43. Proceedings of a conference on: Analysis & Computational Mathematics. 18–19 September 2008, Notre Dame University, Lebanon. Research Publishing Services, Singapore. (together with E. Saleeby).