Dr. Robert Schippa
- Kollegiengebäude Mathematik (20.30)
- rschippa@kias.re.kr
- 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
Semester | Titel | Typ |
---|---|---|
Sommersemester 2022 | Proseminar Analysis | Proseminar |
Research interests
- nonlinear dispersive equations
- Harmonic Analysis on Euclidean space
- quasilinear wave equations
Publications
- Generalized inhomogeneous Strichartz estimates. Discrete and Continuous Dynamical Systems - Series A (2017) Vol. 37, No. 6, pp. 3387-3410. Link
- Sharp Strichartz estimates in spherical coordinates. Communications on Pure and Applied Analysis (2017) Vol. 16, No. 6, pp. 2047-2051. Link
- On the existence of periodic solutions to the modified Korteweg–de Vries equation. Journal of Evolution Equations (2020) Vol. 20, pp.725-776 Link
- On Strichartz estimates from decoupling and applications. Mathematics of Wave Phenomena Link
- Local and global well-posedness for dispersion generalized Benjamin-Ono equations on the circle. Nonlinear Analysis:TMA. (2020). Vol. 196 Link
- On short-time bilinear Strichartz estimates and applications to the Shrira equation. Nonlinear Analysis: TMA. (2020) Vol. 198 Link
- 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
- (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
- (w/ Friedrich Klaus) A priori estimates for the derivative nonlinear Schrödinger equation. Funkcialaj Ekvacioj (2022) Vol. 65, No. 3, pp. 329--346 Link
- (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
- A priori estimates of periodic solutions to the modified Benjamin-Ono equation. Journal of Differential Equations (2021) Vol. 299, 111-153 Link
- (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)
- On smoothing estimates in modulation spaces and the NLS with slowly decaying initial data. Journal of Functional Analysis (2022), Vol. 282 (5) Link
- Resolvent estimates for time-harmonic Maxwell's equations in the partially anisotropic case. Journal of Fourier Analysis and Applications (2022), Vol. 28 (2) Link
- (w/ Roland Schnaubelt) On quasilinear Maxwell equations in two dimensions. Pure Appl. Anal. 4 (2022), no. 2, 313–365. Link
- (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
- 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
- (w/ Jan Rozendaal) Nonlinear wave equations with slowly decaying initial data. (accepted to Journal of Differential Equations) Link to Preprint
- Oscillatory integral operators with homogeneous phase functions. (accepted to Journal d'Analyse) Link to Preprint
- (w/ Dorothee Frey) Strichartz estimates for equations with structured Lipschitz coefficients. (accepted to Journal of Evolution Equations) Link to Preprint
- (w/ Roland Schnaubelt) Strichartz estimates for Maxwell equations in media: the fully anisotropic case. (accepted to Journal of Hyperbolic Differential Equations) Link to Preprint
- (w/ Akansha Sanwal) Low regularity well-posedness for KP-I equations: the dispersion generalised case (accepted to Nonlinearity) Link to Preprint
- (w/ Roland Schnaubelt) Strichartz estimates for Maxwell equations in media: the structured two-dimensional case Archiv der Mathematik Link
Preprints
- (w/ Anna Muranova) Eigenvalues of the normalized complex Laplacian on finite electrical networks.Link to Preprint
- Strichartz estimates for Maxwell equations in media: the partially anisotropic case. Link to Preprint
- (w/ Sebastian Herr and Akansha Sanwal) Low regularity well-posedness for KP-I equations: the three-dimensional case Link to Preprint
- (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