Jerome Wettstein


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Wettstein

First Name

Jerome

ORCID

0000-0002-0756-279X

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Publications 1 - 6 of 6
  • Critical local and nonlocal PDEs and improved Regularity Results
    Item type: Doctoral Thesis
    Wettstein, Jerome (2022)
  • Integrability by compensation for Dirac Equation
    Item type: Working Paper
    Da Lio, Francesca; Rivière, Tristan; Wettstein, Jerome (2021)
    arXiv
    We consider the Dirac Operator acting on the Clifford Algebra Cℓm. We show that under critical assumptions on the potential and the spinor field the equation is subject to an integrability by compensation phenomenon and has a sub-critical behaviour below some positive energy threshold (i.e. ϵ−regularity theorem). This extends in 4 space dimensions as well as in 3 dimensions a similar result obtained previously by the two first authors in 2 D in \cite{DLR1}.
  • Uniqueness and regularity of the fractional harmonic gradient flow in Sⁿ⁻¹
    Item type: Journal Article
    Wettstein, Jerome (2022)
    Nonlinear Analysis
    In this paper, we study the fractional harmonic gradient flow on S¹ taking values in Sⁿ⁻¹ ⊂ Rⁿ for every n ≥ 2, in particular addressing uniqueness and regularity of solutions in the so-called energy class with sufficiently small energy, adding to the existing body of knowledge which includes existence of solutions, see Schikorra et al. (2017), and bubbling phenomena as studied by Sire et al. (0000). We extend the techniques by Struwe (1985) and Rivière (1993) to the non-local framework and exploit integrability by compensation properties due to fractional Wente-type inequalities as in Mazowiecka and Schikorra (2018). Moreover, we briefly discuss convergence properties for solutions to the fractional gradient flow as t → ∞.
  • Bergman-Bourgain-Brezis-type inequality
    Item type: Journal Article
    Da Lio, Francesca; Rivière, Tristan; Wettstein, Jerome (2021)
    Journal of Functional Analysis
    In this note, we prove a fractional version in 1-D of the Bourgain-Brezis inequality [1]. We show that such an inequality is equivalent to the fact that a holomorphic function f:D→C belongs to the Bergman space A2(D), namely f∈L2(D), if and only if ‖f‖L1+H−1/2(S1):=limsupr→1−‖f(reiθ)‖L1+H−1/2(S1)<+∞. Possible generalisations to the higher-dimensional torus are explored.
  • Integrability by compensation for Dirac equation
    Item type: Journal Article
    Da Lio, Francesca; Rivière, Tristan; Wettstein, Jerome (2022)
    Transactions of the American Mathematical Society
    We consider the Dirac operator acting on the Clifford algebra Cl-m. We show that under critical assumptions on the potential and the spinor field the equation is subject to an integrability by compensation phenomenon and has a sub-critical behaviour below some positive energy threshold (i.e. epsilon- regularity theorem). This extends in 4 space dimension as well as in 3 dimension a similar result obtained previously by the two first authors in 2D in F. Da Lio and T. Rivi ' ere [Critical chirality in elliptic systems, Ann. Inst. H. Poincare Anal. Non Lin ' eaire, 38 (2021), no. 5, 1373-1405].
  • Bergaman-Bourgain-Brezis type inequality
    Item type: Working Paper
    Da Lio, Francesca; Rivière, Tristan; Wettstein, Jerome (2020)
    arXiv
Publications 1 - 6 of 6