Yannick Sire

1. Nonlinear equations for fractional Laplacians I: Regularity, maximum\n principles, and Hamiltonian estimates
   2010/12/03 by Xavier Cabré, Yannick Sire, Cabre, Xavier +1 · 25 citations
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
2. Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities
   2014/02/18 by Luis Caffarelli, Tianling Jin, Yannick Sire +1 · 6 citations
   Mathematics · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Fractional Differential Equations Solutions
3. Convexity of level sets for elliptic problems in convex domains or convex rings: two counterexamples
   2013/04/11 by François Hamel, Nikolaï Nadirashvili, Hamel, Francois +3 · 3 citations
   Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations
4. Asymptotics for the fractional Allen-Cahn equation and stationary nonlocal minimal surfaces
   2016/10/23 by Vincent Millot, Millot, Vincent, Yannick Sire +3 · 3 citations
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations
5. Nonlinear equations for fractional Laplacians II: existence, uniqueness, and qualitative properties of solutions
   2011/11/03 by Xavier Cabré, Yannick Sire, Cabre, Xavier +1 · 2 citations
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
6. A new class of Traveling Solitons for cubic Fractional Nonlinear Schrodinger equations
   2015/01/07 by Younghun Hong, Hong, Younghun, Yannick Sire +1 · 2 citations
   Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
7. Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
   2008/01/15 by Yannick Sire, Enrico Valdinoci, Sire, Yannick +1 · 1 citation
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
8. Quasimode, eigenfunction and spectral projection bounds for\n Schr "odinger operators on manifolds with critically singular potentials
   2019/04/21 by Matthew D. Blair, Yannick Sire, Blair, Matthew D. +3 · 1 citation
   Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
9. On the Bär-Hijazi-Lott invariant for the Dirac operator and a spinorial proof of the Yamabe problem
   2021/12/07 by Yannick Sire, Tian Xu, Sire, Yannick +1 · 1 citation
   Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Crystallography and Radiation Phenomena #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics
10. The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees
    2024/12/01 by Jean-Philippe Anker, Guendalina Palmirotta, Anker, Jean-Philippe +3 · 1 citation
    Mathematics · #Advanced Mathematical Physics Problems
11. Giga-Kohn-type results for the fully fractional heat equation
    2026/07/18 by Yannick Sire, Juncheng Wei, Ke Wu +1
    #math.AP