Thomas Kappeler
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Thomas Kappeler has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
- Riccardo Montalto
Dipartimento di Matematica “Federigo Enriques”, Università degli studi di Milano, Milano, Italy
8 shared publications - Patrick Gérard
Université Paris-Saclay, Orsay, France
7 shared publications - Michiel van Den Berg
School of Mathematics, University of Bristol, Bristol, UK
6 shared publications - Peter Topalov
Northeastern University
4 shared publications - Daniel C. Cohen
Louisiana State University
3 shared publications - Peter Topalov
Northeastern University, Boston, USA
3 shared publications
Latest Publications
- Open Access
On efficiency and localisation for the torsion function
We consider the torsion function for the Dirichlet Laplacian $-\Delta$, and for the Schr\"odinger operator $- \Delta + V$ on an open set $\Omega\subset \R^m$ of finite Lebesgue measure $0<|\Omega|<\infty$ with a real-valued, non-negative, measurable potential $V.$ We investigate the efficiency and the phenomenon of localisation for the torsion function, and their interplay with the geometry of the first Dirichlet eigenfunction.Open AccessOn efficiency and localisation for the torsion function
We consider the torsion function for the Dirichlet Laplacian $-\Delta$, and for the Schr\"odinger operator $- \Delta + V$ on an open set $\Omega\subset \R^m$ of finite Lebesgue measure $0<|\Omega|<\infty$ with a real-valued, non-negative, measurable potential $V.$ We investigate the efficiency and the phenomenon of localisation for the torsion function, and their interplay with the geometry of the first Dirichlet eigenfunction. - Open Access
- 1 January 2023
- Published by International Press of Boston in Acta Mathematica
- Vol. 231 (1) , 31-88
Sharp well-posedness results of the Benjamin–Ono equation in $H^s (\mathbb{T}, \mathbb{R})$ and qualitative properties of its solutionsInternational Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2023
- Published by International Press of Boston in Acta Mathematica
- Vol. 231 (1) , 31-88
Open AccessSharp well-posedness results of the Benjamin–Ono equation in $H^s (\mathbb{T}, \mathbb{R})$ and qualitative properties of its solutionsInternational Press of Boston - publishers of scholarly mathematical and scientific journals and books
- Open Access
- 1 December 2022
- Published by Springer Nature in Potential Analysis
- Vol. 57 (4) , 571-600
On Efficiency and Localisation for the Torsion Function
- 1 December 2022
- Published by Springer Nature in Potential Analysis
- Vol. 57 (4) , 571-600
Open AccessOn Efficiency and Localisation for the Torsion Function
- 1 March 2022
- Published by Elsevier in Nonlinear Analysis
- Vol. 216
On the analytic Birkhoff normal form of the Benjamin–Ono equation and applications
- 1 March 2022
- Published by Elsevier in Nonlinear Analysis
- Vol. 216
On the analytic Birkhoff normal form of the Benjamin–Ono equation and applications
- Open Access
- 1 January 2022
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 42 (9) , 4127-4201
Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators
Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the Benjamin-Ono equation on the torus having the following two main properties: (1) up to a remainder term, which is smoothing to any given order, the coordinate transformation is a pseudo-differential operator of order 0 with principal part given by a modified Fourier transform (modification by a phase factor) and (2) the pullback of the Hamiltonian of the Benjamin-Ono is in normal form up to order three and the corresponding Hamiltonian vector field admits an expansion in terms of para-differential operators. Such coordinates are a key ingredient for studying the stability of finite gap solutions of the Benjamin-Ono equation under small, quasi-linear perturbations.
- 1 January 2022
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 42 (9) , 4127-4201
Open AccessNormal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators
Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the Benjamin-Ono equation on the torus having the following two main properties: (1) up to a remainder term, which is smoothing to any given order, the coordinate transformation is a pseudo-differential operator of order 0 with principal part given by a modified Fourier transform (modification by a phase factor) and (2) the pullback of the Hamiltonian of the Benjamin-Ono is in normal form up to order three and the corresponding Hamiltonian vector field admits an expansion in terms of para-differential operators. Such coordinates are a key ingredient for studying the stability of finite gap solutions of the Benjamin-Ono equation under small, quasi-linear perturbations.
- Open Access
On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus
We investigate the spectrum of the Lax operator $L_u$ of the Benjamin-Ono equation on the torus for complex valued potentials $u$ in the Sobolev space $H^{-s}(\mathbb{T},\mathbb{C})$, $0 \le s < 1/2$, with small imaginary part and prove analytic properties of the moment map, defined in terms of spectral data of $L_u$.Open AccessOn the spectrum of the Lax operator of the Benjamin-Ono equation on the torus
We investigate the spectrum of the Lax operator $L_u$ of the Benjamin-Ono equation on the torus for complex valued potentials $u$ in the Sobolev space $H^{-s}(\mathbb{T},\mathbb{C})$, $0 \le s < 1/2$, with small imaginary part and prove analytic properties of the moment map, defined in terms of spectral data of $L_u$. - Open Access
- 11 May 2021
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 385 (3) , 1871-1956
On the Stability of Periodic Multi-Solitons of the KdV Equation
In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size $$\varepsilon > 0$$ , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least $$O(\varepsilon ^{-2})$$ . To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE.- 11 May 2021
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 385 (3) , 1871-1956
Open AccessOn the Stability of Periodic Multi-Solitons of the KdV Equation
In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size $$\varepsilon > 0$$ , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least $$O(\varepsilon ^{-2})$$ . To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE. - Open Access
- 1 April 2021
- Published by Wiley in Mathematika
- Vol. 67 (2) , 514-531
LOCALIZATION FOR THE TORSION FUNCTION AND THE STRONG HARDY INEQUALITY
- 1 April 2021
- Published by Wiley in Mathematika
- Vol. 67 (2) , 514-531
Open AccessLOCALIZATION FOR THE TORSION FUNCTION AND THE STRONG HARDY INEQUALITY
- Open Access
On the stability of periodic multi-solitons of the KdV equation
In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size $\varepsilon > 0$, a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least $O(\varepsilon^{-2})$. To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE.Open AccessOn the stability of periodic multi-solitons of the KdV equation
In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size $\varepsilon > 0$, a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least $O(\varepsilon^{-2})$. To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE. - 4 January 2021
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 239 (3) , 1395-1500
Large KAM Tori for Quasi-linear Perturbations of KdV
- 4 January 2021
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 239 (3) , 1395-1500
Large KAM Tori for Quasi-linear Perturbations of KdV