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Dr. Robert Schippa

Dr. Robert Schippa

  • Project A5: Qualitative behavior of nonlinear Maxwell equations

  •

Postdoctoral researcher within the CRC 1173, Project A5, 1 April 2020 - 30 June 2023
This homepage will not be updated anymore. Please visit my new Homepage

Current List of Courses
Semester Titel Typ
Summer Semester 2022 Proseminar

Research interests

  • nonlinear dispersive equations
  • Harmonic Analysis on Euclidean space
  • quasilinear wave equations

Publications

  1. Generalized inhomogeneous Strichartz estimates. Discrete and Continuous Dynamical Systems - Series A (2017) Vol. 37, No. 6, pp. 3387-3410. Link
  2. Sharp Strichartz estimates in spherical coordinates. Communications on Pure and Applied Analysis (2017) Vol. 16, No. 6, pp. 2047-2051. Link
  3. On the existence of periodic solutions to the modified Korteweg–de Vries equation. Journal of Evolution Equations (2020) Vol. 20, pp.725-776 Link
  4. On Strichartz estimates from decoupling and applications. Mathematics of Wave Phenomena Link
  5. Local and global well-posedness for dispersion generalized Benjamin-Ono equations on the circle. Nonlinear Analysis:TMA. (2020). Vol. 196 Link
  6. On short-time bilinear Strichartz estimates and applications to the Shrira equation. Nonlinear Analysis: TMA. (2020) Vol. 198 Link
  7. On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations. Discrete and Continuous Dynamical Systems - Series A (2020) Vol. 40, No. 9, pp.5189-5215 Link
  8. (w/ Shinya Kinoshita) Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation. Journal of Functional Analysis (2021) Vol. 280, No. 6 Link
  9. (w/ Friedrich Klaus) A priori estimates for the derivative nonlinear Schrödinger equation. Funkcialaj Ekvacioj (2022) Vol. 65, No. 3, pp. 329--346 Link
  10. (w/ Kihyun Kim) Low regularity well-posedness for generalized Benjamin-Ono equations on the circle. J. Hyperbolic Differ. Equ. 18 (2021), no. 4, 931–984. Link
  11. A priori estimates of periodic solutions to the modified Benjamin-Ono equation. Journal of Differential Equations (2021) Vol. 299, 111-153 Link
  12. (w/ Rainer Mandel) Time-harmonic solutions for Maxwell's equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces. Link (Annales Henri Poincar'e: Journal of Mathematical and Theoretical Physics)
  13. On smoothing estimates in modulation spaces and the NLS with slowly decaying initial data. Journal of Functional Analysis (2022), Vol. 282 (5) Link
  14. Resolvent estimates for time-harmonic Maxwell's equations in the partially anisotropic case. Journal of Fourier Analysis and Applications (2022), Vol. 28 (2) Link
  15. (w/ Roland Schnaubelt) On quasilinear Maxwell equations in two dimensions. Pure Appl. Anal. 4 (2022), no. 2, 313–365. Link
  16. (w/ Jean-Claude Cuenin) Fourier transform of surface-carried measures of two-dimensional generic surfaces and applications. Commun. Pure Appl. Anal. 21 (2022), no. 9, 2873–2889. Link
  17. Infinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces. J. Math. Anal. Appl. 519 (2023), no. 1, Paper No. 126748, 14 pp. Link
  18. (w/ Jan Rozendaal) Nonlinear wave equations with slowly decaying initial data. (accepted to Journal of Differential Equations) Link to Preprint
  19. Oscillatory integral operators with homogeneous phase functions. (accepted to Journal d'Analyse) Link to Preprint
  20. (w/ Dorothee Frey) Strichartz estimates for equations with structured Lipschitz coefficients. (accepted to Journal of Evolution Equations) Link to Preprint
  21. (w/ Roland Schnaubelt) Strichartz estimates for Maxwell equations in media: the fully anisotropic case. (accepted to Journal of Hyperbolic Differential Equations) Link to Preprint
  22. (w/ Akansha Sanwal) Low regularity well-posedness for KP-I equations: the dispersion generalised case (accepted to Nonlinearity) Link to Preprint
  23. (w/ Roland Schnaubelt) Strichartz estimates for Maxwell equations in media: the structured two-dimensional case Archiv der Mathematik Link

Preprints

  1. (w/ Anna Muranova) Eigenvalues of the normalized complex Laplacian on finite electrical networks.Link to Preprint
  2. Strichartz estimates for Maxwell equations in media: the partially anisotropic case. Link to Preprint
  3. (w/ Sebastian Herr and Akansha Sanwal) Low regularity well-posedness for KP-I equations: the three-dimensional case Link to Preprint
  4. (w/ Nicolas Burq) Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions https://arxiv.org/abs/2304.13368

Doctoral thesis

Short-time Fourier transform restriction phenomena and applications to nonlinear dispersive equations (Bielefeld University, 09/ 2019). Link