Dr. Sven Jarohs

Current Position: Coordinator of Studies.

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

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. "Gradient estimates in fractional Dirichlet problems" joint with Mouhamed Moustapha Fall, preprint available online at [ArXiv] (2019)
  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. "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)
  2. "Semilinear Dirichlet problem for the fractional Laplacian" joint with Krzysztof Bogdan and Edyta Kania, to appear in Nonlinear Analysis (2019).
  3. "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)
  4. "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)
  5. "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)
  6. "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)
  7. "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.
  8. "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)
  9. "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)
  10. "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.
  11. "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)
  12. "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)
  13. "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)
  14. "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)
  15. "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)