Dr. Sven Jarohs

Current Position: Coordinator of Studies.

Department of Mathematics and Computer Sciences,
Goethe-University Frankfurt am Main.

Office hours (during lecture time): ---

Contact:

Tel: 069/798-23531
jarohs@math.uni-frankfurt.de
Robert-Mayer-Straße 10, Raum 904
D-60325 Frankfurt am Main

 

Teaching:

Complete teaching list.

Applied Analysis and Numerics Seminar


Research interests:

Nonlocal problems and nonlocal diffusion equations, long-time behavior of solutions,
geometric and regularity related properties of solutions, maximum principles.


Recent and upcoming Talks/Conferences:

Complete list of past talks and conferences.

Preprints:

  1. "Fractional Laplacians on ellipsoids" joint with Nicola Abatangelo and Alberto Saldana, preprint available online at [ArXiv] (2020)
  2. "Foliated Schwarz symmetry of solutions to a cooperative system of equations involving nonlocal operators" joint with Antonio Greco, preprint available online at [ArXiv] (2019)
  3. "A new look at the fractional Poisson problem via the Logarithmic Laplacian" joint with Alberto Saldana and Tobias Weth, preprint available online at [ArXiv] (2019)

Publications:

  1. "Gradient estimates in fractional Dirichlet problems" joint with Mouhamed Moustapha Fall, to appear in Potential Analysis (2020), preprint available online at [ArXiv] (2019)
  2. "On overdetermined problems for a general class of nonlocal operators" joint work with Anup Biswas, to appear in Journal of Differential Equations [doi], preprint available online at [ArXiv] (2019)
  3. "Semilinear Dirichlet problem for the fractional Laplacian" joint with Krzysztof Bogdan and Edyta Kania, to appear in Nonlinear Analysis [doi] (2019).
  4. "Local compactness and nonvanishing for weakly singular nonlocal quadratic forms" joint with Tobias Weth, to appear in Nonlinear Analysis [doi], preprint available online at [ArXiv] (2018)
  5. "Starshape of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings" joint with Tadeusz Kulczycki and Paolo Salani, to appear in Mathematische Nachrichten [doi], preprint available online at [ArXiv] (2017)
  6. "On the maximum principle for nonlocal operators" joint with Tobias Weth, Mathematische Zeitschrift 293.1 (2019), 81--111 [doi], preprint available online at [ArXiv] (2017)
  7. "Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions" joint work with Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall, and Alberto Saldana, to appear in Discrete and Continuous Dynamical Systems - Series A, preprint available online at [ArXiv] (2018)
  8. "Green function and Martin kernel for higher-order fractional Laplacians in balls" joint with Nicola Abatangelo and Alberto Saldana,
    Nonlinear Analysis 175 (2018), 173--190 [doi], extended preprint available online at [ArXiv] (2016)
    Addendum.
  9. "On the loss of maximum principles for higher-order fractional Laplacians" joint with Nicola Abatangelo and Alberto Saldana,
    Proceedings of the American Mathematical Society 146.11 (2018), 4823--4835, extended preprint available online at [ArXiv] (2016)
  10. "Positive powers of the Laplacian: from hypersingular integrals to boundary value problems" joint with Nicola Abatangelo and Alberto Saldana, Communications on Pure and Applied Analysis 17.3 (2018), 899--922, preprint available online at [ArXiv] (2017)
  11. "Integral representation of solutions to higher-order fractional Dirichlet problems on balls" joint with Nicola Abatangelo and Alberto Saldana, to appear in Communications in Contemporary Mathematics [doi], preprint available online at [ArXiv] (2017)
    Addendum.
  12. "Strong comparison principle for the fractional p-Laplacian and applications to starshaped rings", Advanced Nonlinear Studies 18.4 (2018), 691--704 [doi], preprint available online at [ArXiv] (2017)
  13. "Symmetry of solutions to nonlocal nonlinear boundary value problems in radial sets",
    Nonlinear Differential Equations and Applications 23.3 (2016), 1--22, preprint available online at [ArXiv] (2015)
  14. "Symmetry via antisymmetric maximum principles in nonlocal problems of variable order" joint with Tobias Weth,
    Annali di Matematica Pura ed Applicata (4) 195.1 (2016), 273-291 [doi], preprint available online at [ArXiv] (2014)
  15. "Overdetermined problems with fractional Laplacian" joint with Mouhamed Moustapha Fall,
    ESAIM: Control, Optimisation and Calculus of Variations 21.4 (2015), 924--938, preprint available online at [ArXiv] (2014)
  16. "Asymptotic symmetry for a class of nonlinear fractional reaction diffusion equations" joint with Tobias Weth,
    Discrete and Continuous Dynamical Systems - Series A 34.6 (2014), 2581--2615, preprint available online at [ArXiv] (2013)

Dissertation:

"Symmetry via maximum principles for nonlocal nonlinear boundary value problems" doctoral thesis, Goethe University Frankfurt (2015) (see here)