Ros-Oton, Xavier

1. The Dirichlet problem for the fractional Laplacian: regularity up to the\n boundary
   2012/07/25 by Xavier Ros‐Oton, Ros-Oton, Xavier, Joaquim Serra +1 · 31 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
2. Regularity theory for general stable operators
   2014/12/12 by Ros-Oton, Xavier, Serra, Joaquim · 14 citations
   #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
3. Nonlocal problems with Neumann boundary conditions
   2014/07/11 by Dipierro, Serena, Ros-Oton, Xavier, Valdinoci, Enrico · 10 citations
   #Analysis of PDEs (math.AP) #FOS: Mathematics
4. The Pohozaev identity for the fractional Laplacian
   2012/07/25 by Xavier Ros‐Oton, Joaquim Serra, Ros-Oton, Xavier +1 · 7 citations
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations
5. Nonlocal elliptic equations in bounded domains: a survey
   2015/04/16 by Xavier Ros‐Oton, Ros-Oton, Xavier · 7 citations
   Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR)
6. Nonexistence results for nonlocal equations with critical and supercritical nonlinearities
   2013/09/20 by Ros-Oton, Xavier, Serra, Joaquim · 6 citations
   #Analysis of PDEs (math.AP) #FOS: Mathematics
7. Sharp isoperimetric inequalities via the ABP method
   2013/04/05 by Cabre, Xavier, Ros-Oton, Xavier, Serra, Joaquim · 4 citations
   #49Q20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 28A75 #Secondary 35A23
8. Global regularity for the free boundary in the obstacle problem for the fractional Laplacian
   2015/06/15 by Barrios, Begoña, Figalli, Alessio, Ros-Oton, Xavier · 4 citations
   #Analysis of PDEs (math.AP) #FOS: Mathematics
9. The extremal solution for the fractional Laplacian
   2013/05/11 by Xavier Ros‐Oton, Ros-Oton, Xavier, Joaquim Serra +1 · 3 citations
   Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
10. Boundary regularity for the fractional heat equation
    2014/11/30 by Xavier Fernández‐Real, Xavier Ros‐Oton, Fernández-Real, Xavier +1 · 3 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
11. Regularity theory for general stable operators: parabolic equations
    2015/11/19 by Fernández-Real, Xavier, Ros-Oton, Xavier · 3 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
12. Obstacle problems for integro-differential operators: Higher regularity of free boundaries
    2019/09/23 by Abatangelo, Nicola, Ros-Oton, Xavier · 4 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
13. Sharp quantitative stability for isoperimetric inequalities with homogeneous weights
    2020/06/24 by Cinti, Eleonora, Glaudo, Federico, Pratelli, Aldo +2 · 4 citations
    #28A75 #49K40 (Secondary) #49Q10 (Primary) 49Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
14. Sobolev and isoperimetric inequalities with monomial weights
    2012/10/16 by Cabre, Xavier, Ros-Oton, Xavier · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
15. The singular set in the Stefan problem
    2021/03/24 by Figalli, Alessio, Ros-Oton, Xavier, Serra, Joaquim · 3 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
16. Stable solutions to semilinear elliptic equations are smooth up to\n dimension 9
    2019/07/22 by Xavier Cabré, Alessio Figalli, Cabre, Xavier +5 · 3 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
17. The boundary Harnack principle for nonlocal elliptic operators in non-divergence form
    2016/10/18 by Ros-Oton, Xavier, Serra, Joaquim · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics
18. Optimal regularity for nonlocal elliptic equations and free boundary problems
    2024/03/12 by Xavier Ros‐Oton, Marvin Weidner, Ros-Oton, Xavier +1 · 4 citations
    Computer Science · Mathematics · #31B05 #35B65 #35K90 #47G20 #60J75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems
19. Non-symmetric stable operators: regularity theory and integration by parts
    2020/12/09 by Serena Dipierro, Xavier Ros‐Oton, Dipierro, Serena +5 · 2 citations
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
20. Improvement of flatness for nonlocal free boundary problems
    2024/04/24 by Ros-Oton, Xavier, Weidner, Marvin · 3 citations
    #31B05 #35B65 #35R35 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics
21. Euclidean balls solve some isoperimetric problems with nonradial weights
    2012/10/05 by Xavier Cabré, Xavier Ros‐Oton, Cabre, Xavier +3 · 1 citation
    Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Point processes and geometric inequalities
22. Local integration by parts and Pohozaev identities for higher order\n fractional Laplacians
    2014/06/04 by Xavier Ros‐Oton, Joaquim Serra, Ros-Oton, Xavier +1 · 1 citation
    Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations
23. Free boundary regularity in the parabolic fractional obstacle problem
    2016/05/02 by Barrios, Begoña, Figalli, Alessio, Ros-Oton, Xavier · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
24. Infinite speed of propagation and regularity of solutions to the\n fractional porous medium equation in general domains
    2015/10/13 by Matteo Bonforte, Alessio Figalli, Bonforte, Matteo +3 · 1 citation
    Computer Science · Mathematics · #35B65 #35K55 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
25. Obstacle problems and free boundaries: an overview
    2017/07/04 by Ros-Oton, Xavier · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
26. Boundary regularity, Pohozaev identities, and nonexistence results
    2017/05/16 by Ros-Oton, Xavier · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
27. Regularity for nonlocal equations with local Neumann boundary conditions
    2024/03/26 by Ros-Oton, Xavier, Weidner, Marvin · 2 citations
    #31B05 #35B44 #35B65 #35R53 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics
28. On global solutions to semilinear elliptic equations related to the\n one-phase free boundary problem
    2018/11/07 by Xavier Fernández‐Real, Fernández-Real, Xavier, Xavier Ros‐Oton +1 · 1 citation
    Computer Science · Mathematics · #35B07 #35J91 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
29. The Neumann problem for the fractional Laplacian: regularity up to the boundary
    2020/06/17 by Alessandro Audrito, Audrito, Alessandro, Juan-Carlos Felipe-Navarro +3 · 1 citation
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
30. New boundary Harnack inequalities with right hand side
    2020/10/02 by Ros-Oton, Xavier, Torres-Latorre, Clara · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
31. Extinction rates for nonradial solutions to the Stefan problem
    2025/04/09 by Fioravanti, Gabriele, Ros-Oton, Xavier, Torres-Latorre, Clara · 2 citations
    #35B65 #35K55 #35R35 #80A22 #Analysis of PDEs (math.AP) #FOS: Mathematics
32. Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels
    2023/08/22 by Xavier Fernández‐Real, Fernández-Real, Xavier, Xavier Ros‐Oton +1 · 1 citation
    Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems
33. Optimal regularity for kinetic Fokker-Planck equations in domains
    2025/05/17 by Xavier Ros‐Oton, Marvin Weidner, Ros-Oton, Xavier +1 · 3 citations
    Mathematics · #35B65 #35Q84 #82C40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations