Siegfried Carl
Professor of Mathematics

siegfried_carl Contact Phone +49 345 5524639 Fax +49 345 5527003 Email siegfried.carl@mathematik.uni-halle.de
Postal Address Prof. Dr. Siegfried Carl Martin-Luther-Universität Halle-Wittenberg Institut für Mathematik 06099 Halle, Germany
Research Interests Nonlinear Analysis Nonsmooth Variational Problems
(Variational- and Hemivariational Inequalities)
Nonlinear Elliptic and Parabolic Differential Equations and Inclusions Comparison Principles Multiple Solutions in Nonlinear Elliptic Problems Nonlinear Eigenvalue Problems
Siegfried Carl - Professor of Mathematics
Curriculum Vitae

Education
  • 1975 Master in Mathematics (Diploma in Mathematics), University of Halle, Germany
  • 1984 Ph.D. in Mathematics (Dr.rer.nat.), University of Halle, Germany
  • 1990 postdoctoral qualification - Dr.rer.nat.habil. (Habilitation), Department of Mathematics and Computer Science, Institute of Technology (Technische Hochschule), Merseburg, Germany
Employment
  • 1975-1981 Researcher, Academy of Science Institute of Solid State Physics and Electron Microscopy, Halle, Germany
  • 1981-1984 Ph.D.-Research Fellow, Department of Mathematics, University of Halle, Germany
  • 1984-1993 Assistant and Senior Assistant, Department of Mathematics and Computer Science, Institute of Technology, Merseburg, Germany
  • 1993-1995 Privatdozent, Department of Mathematics and Computer Science, University of Halle, Germany
  • since 1995 Professor of Mathematics, Institute of Mathematics, University of Halle, Germany
Visiting Positions (A selection of stays of one month and longer)
  • 1990 (1 month) Department of Mathematics, University of Oulu, Finland
  • 1994 (2 months) Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL, USA
  • 1994, LEOPOLDINA-RESEARCH GRANT AWARD from GERMAN ACADEMY OF SCIENCES LEOPOLDINA (including a Leopoldina Scholarship for a 6-months research stay abroad)
  • 1995 (6 months) Department of Mathematics, North Carolina State University, Raleigh, USA
  • 1996 (1 month) Department of Mathematics, University of Oulu, Finland
  • 1997 (1 month) Department of Mathematics, University of Oulu, Finland
  • 1998 (5 weeks) Department of Mathematics, University of Oulu, Finland
  • 2000 (1 month) Department of Mathematical Sciences, University of Delaware, USA and Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL, USA
  • 2001-2002 (1 academic year) Visiting Professor at the Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL, USA
  • 2005 (1 month) Visiting Professor at the Department of Mathematics, University of Perpignan, France
  • 2008 (1 month) Visiting Professor at the Department of Mathematics, University of Perpignan, France
Siegfried Carl - Professor of Mathematics
Publications

Monographs
Recent Research Articles (a list of all publications as pdf-file can be downloaded here)
  1. Carl, S., N-Laplacian elliptic equations in exterior domains via Kelvin transform, Pure and Applied Functional Analysis (in: Special Issue of the journal Pure and Applied Functional Analysis dedicated to Professor H. Brezis) to appear
  2. Carl, S., and Vy K. Le, Extremal solutions of multi-valued variational inequalities in plane exterior domains, J. Differential Equations (2019), https://doi.org/10.1016/j.jde.2019.05.020
  3. Carl, S., Costa, David G., Fotouhi, M., and Tehrani, H., Invariance of critical points under Kelvin transform and multiple solutions in exterior domains of R^2, Calc. Var. Partial Differential Equations 58 (2019), no. 2, Art. 65, 24 pp.
  4. Carl, S., Costa, David G., and Tehrani, H., Extremal solutions of logistic-type equations in exterior domain in R^2, Nonlinear Anal. 176 (2018), 272-287.
  5. Carl, S., Tietz, Ch., Quasilinear elliptic equations with measures and multi-valued lower order terms, Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 2, 193-212.
  6. Carl, S., Decay estimates for Wolff potentials in R^N and gradient-dependent quasilinear elliptic equations, J. Differential Equations 265 (2018), no. 8, 3685-3708.
  7. Carl, S., and Motreanu, D., Extremal solutions for quasilinear parabolic systems in trapping regions, Pure and Applied Functional Analysis 3 (2018), no. 1, 57-74.
  8. Carl, S., Costa, David G., and Tehrani, H., D^{1,2}(R^N) versus C(R^N) local minimizer on manifolds and multiple solutions for zero-mass equations in R^N, Advances in Calculus of Variations 11 (2018), no. 3, 257-272.
  9. Carl, S., Extremal solutions of p-Laplacian problems in D^{1,p}(R^N) via Wolff potential estimates, J. Differential Equations 263 (2017), 3370-3395.
  10. Carl, S., and Motreanu, D., Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions, Monatsh Math 182 (2017), no. 4, 801-821.
  11. Carl, S., Costa, David G., and Tehrani, H., D^{1,2}(R^N) versus C(R^N) local minimizer and a Hopf-type maximum principle, J. Differential Equations 261 (2016), 2006-2025.
  12. Carl, S., Costa, David G., and Tehrani, H., Extremal and sign-changing solutions of supercritical logistic-type equations in R^N, Calc. Var. Partial Differential Equations 54 (2015), no. 4, 4143-4164.
  13. Carl, S., Barrier solutions of elliptic variational inequalities, Nonlinear Anal. Real World Appl. 26 (2015), 75-92.
  14. Carl, S., and Motreanu, D., Multiple solutions for elliptic systems via trapping regions and related nonsmooth potentials, Appl. Anal. 94 (2015), no. 8, 1594-1613.
  15. Carl, S., and D'Ambrosio, L., Foreword [Nonlinear partial differential equations, in honor of Enzo Mitidieri on his 60th birthday], Nonlinear Anal. 121 (2015), 1-2.
  16. Carl, S., and Vy K. Le, Elliptic inequalities with multi-valued operators: existence, comparison and related variational-hemivariational type inequalities, Nonlinear Anal. 121 (2015), 130-152.
  17. Carl, S., and Le, V. K., Multi-Valued Parabolic Variational Inequalities and Related Variational-Hemivariational Inequalities, Advanced Nonlinear Studies 14 (2014), 603-631.
  18. Carl, S., and Le, V. K., Quasilinear Parabolic Variational Inequalities with Multi-Valued Lower Order Terms, Z. Angew. Math. Phys. 65 (2014), 845-864
  19. Carl, S., Existence and Extremal Solutions of Parabolic Variational-Hemivariational Inequalities, Monatsh. Math. 172 (2013), 29-54.
  20. Candito, P., Carl, S., and Livrea, R., Variational versus pseudomonotone operator approach in parameter-dependent nonlinear elliptic problems, Dynam. Systems Appl. 22 (2013), 397-410.
  21. Carl, S., Signorini type variational inequality with state-dependent discontinuous multivalued boundary operators, Nonlinear Anal. 92 (2013), 138-152.
  22. Carl, S., Elliptic variational inequalities with discontinuous multi-valued lower order terms, Adv. Nonlinear Stud. 13 (2013), 55-78.

Siegfried Carl - Professor of Mathematics
Editorial Work

Editorial Board Member of the following international mathematical journals:
Siegfried Carl - Professor of Mathematics
Teaching

The following list provides a selection of courses taught in recent years:
  • Basic courses in Analysis:
    1. Real Analysis in one and higher dimensions
    2. Ordinary Differential Equations
    3. Function Theory of One Complex Variable
    4. Measure Theory
  • Introduction to Linear Functional Analysis
  • Nonlinear Analysis:
    1. Monotone and Pseudomonotone Operators
    2. Variational Inequalities
    3. Variational Methods
  • Partial Differential Equations
  • Functional Analysis and its Applications to Partial Differential Equations
  • Differential Inequalities: Maximum and Comparison Principles
Siegfried Carl - Professor of Mathematics
Projects

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