Dr. Sven Jarohs

Current Position: Coordinator of Studies.

Department of Computer Sciences and Mathematics,
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:

• WS 2022/2023 Mathematics for Physicists 1.
• SS 2022 Mathematics for Physicists 2.
• WS 2021/2022 Ergänzungen zur linearen Funktionalanalysis.
• WS 2021/2022 Mathematics for Physicists 1.
• WS 2020/2021 Mathematics for Physicists 1.
• 26.10.2020 - 30.10.2020 (in digitaler Form) Mathematik Vorkurs (für MathematikerInnen)
• SS 2020 Analysis 1.
• SS 2020 (bis 05.06.) Fractional Sobolev Spaces and Boundary Value Problems.
• 15.04.2020 - 17.04.2020 (in digitaler Form) Mathematik Vorkurs (für MathematikerInnen)

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:

• Seminar on PDEs and applied topics
• Spring School on Local & Nonlocal Elliptic and Geometric Problems, 18. - 22. February 2019 in Mbour, Senegal
• Talk at the Joint meeting, 17. - 20. September 2018 in Wroclaw, Poland
• Cologne Conference on Positivity and Differential Equations, 22. - 25. May 2018 in Cologne, Germany
• Talk at the MIS Final Workshop, 11. - 15. December 2017 in Spa, Belgium

Complete list of past talks and conferences.

Preprints:

1. "Oscillatory Phenomena for Higher-Order Fractional Laplacians" joint with Nicola Abatangelo, preprint available online at [ArXiv] (2022)
2. "On the shape of the first fractional eigenfunction" joint with Nicola Abatangelo, preprint available online at [ArXiv] (2022)

Publications:

1. "Nonradiality of second fractional eigenfunctions of thin annuli" joint with Sidy M. Djitte, to appear in Commun. Pure Appl. Anal. [doi], preprint available online at [ArXiv] (2021)
2. "Nonlocal operators of small order" joint with Pierre Aime Feulefack, to appear in Ann. Mat. Pura Appl. (4), preprint available online at [ArXiv] (2021)
3. "On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian" joint with Tadeusz Kulczycki and Paolo Salani, Nonlinear Anal. 222 (2022), 112956, preprint available online at [ArXiv] (2021)
4. "Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian" joint with Pierre Aime Feulefack and Tobias Weth, J. Fourier Anal. Appl. 28.2 (2022) [doi], preprint available online at [ArXiv] (2021)
5. "Foliated Schwarz symmetry of solutions to a cooperative system of equations involving nonlocal operators" joint with Antonio Greco, J. Elliptic Parabol. Equ. (2022) [doi], preprint available online at [ArXiv] (2019)
6. "Symmetry of odd solutions to equations with fractional Laplacian" joint with Sidy M. Djitte, J. Elliptic Parabol. Equ. (2022) [doi], preprint available online at [ArXiv] (2021)
7. "Fractional Laplacians on ellipsoids" joint with Nicola Abatangelo and Alberto Saldana, Math. Eng. 3.5 (2021), 1--34 [doi], preprint available online at [ArXiv] (2020)
8. "A new look at the fractional Poisson problem via the Logarithmic Laplacian" joint with Alberto Saldana and Tobias Weth, J. Funct. Anal. 279.11 (2020), 108732, preprint available online at [ArXiv] (2019)
9. "Gradient estimates in fractional Dirichlet problems" joint with Mouhamed Moustapha Fall, Potential Anal. 54.4 (2021), 627--636, preprint available online at [ArXiv] (2019)
10. "On overdetermined problems for a general class of nonlocal operators" joint work with Anup Biswas, J. Differential Equations 268.5 (2020), 2368--2393 [doi], preprint available online at [ArXiv] (2019)
11. "Semilinear Dirichlet problem for the fractional Laplacian" joint with Krzysztof Bogdan and Edyta Kania, Nonlinear Anal. 193 (2020), 111512 [doi] (2019).
12. "Local compactness and nonvanishing for weakly singular nonlocal quadratic forms" joint with Tobias Weth, Nonlinear Anal. 193 (2020), 111431 [doi], preprint available online at [ArXiv] (2018)
13. "Starshape of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings" joint with Tadeusz Kulczycki and Paolo Salani, Math. Nachr. 292.5 (2019), 1008--1021 [doi], preprint available online at [ArXiv] (2017)
14. "On the strong maximum principle for nonlocal operators" joint with Tobias Weth, Math. Z. 293.1 (2019), 81--111 [doi], preprint available online at [ArXiv] (2017)
15. "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, Discrete Contin. Dyn. Syst. 39.3 (2019), 1205--1235, preprint available online at [ArXiv] (2018)
16. "Green function and Martin kernel for higher-order fractional Laplacians in balls" joint with Nicola Abatangelo and Alberto Saldana,
    Nonlinear Anal. 175 (2018), 173--190 [doi], extended preprint available online at [ArXiv] (2016)
    Addendum.
17. "On the loss of maximum principles for higher-order fractional Laplacians" joint with Nicola Abatangelo and Alberto Saldana, Proc. Amer. Math. Soc. 146.11 (2018), 4823--4835, extended preprint available online at [ArXiv] (2016)
18. "Positive powers of the Laplacian: from hypersingular integrals to boundary value problems" joint with Nicola Abatangelo and Alberto Saldana, Commun. Pure Appl. Anal. 17.3 (2018), 899--922, preprint available online at [ArXiv] (2017)
19. "Integral representation of solutions to higher-order fractional Dirichlet problems on balls" joint with Nicola Abatangelo and Alberto Saldana, Commun. Contemp. Math. 20.8 (2018), 1850002 [doi], preprint available online at [ArXiv] (2017)
    Addendum.
20. "Strong comparison principle for the fractional p-Laplacian and applications to starshaped rings", Adv. Nonlinear Stud. 18.4 (2018), 691--704 [doi], preprint available online at [ArXiv] (2017)
21. "Symmetry of solutions to nonlocal nonlinear boundary value problems in radial sets", NoDEA Nonlinear Differential Equations Appl. 23.3 (2016), 1--22, preprint available online at [ArXiv] (2015)
22. "Symmetry via antisymmetric maximum principles in nonlocal problems of variable order" joint with Tobias Weth, Ann. Mat. Pura Appl. (4) 195.1 (2016), 273-291 [doi], preprint available online at [ArXiv] (2014)
23. "Overdetermined problems with fractional Laplacian" joint with Mouhamed Moustapha Fall, ESAIM Control Optim. Calc. Var. 21.4 (2015), 924--938, preprint available online at [ArXiv] (2014)
24. "Asymptotic symmetry for a class of nonlinear fractional reaction diffusion equations" joint with Tobias Weth, Discrete Contin. Dyn. Syst. 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)