Integro-Differential Elliptic Equations, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Progress in Mathematics 350, Birkhauser, 2024.
Regularity Theory for Elliptic PDE, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Zurich Lectures in Advanced Mathematics. EMS books, 2022.
C^\infty regularity in semilinear free boundary problems,
Daniel Restrepo, Xavier Ros-Oton,
in preparation (2024).
Regularity for nonlocal equations with local Neumann boundary conditions, pdf
Xavier Ros-Oton, Marvin Weidner,
preprint arXiv (2024).
Optimal regularity for nonlocal elliptic equations and free boundary problems, pdf
Xavier Ros-Oton, Marvin Weidner,
preprint arXiv (2024).
Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
preprint arXiv (2023).
Obstacle problems for nonlocal operators with singular kernels, pdf
Xavier Ros-Oton, Marvin Weidner,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (2024), to appear.
Semiconvexity estimates for nonlinear integro-differential equations, pdf
Xavier Ros-Oton, Clara Torres-Latorre, Marvin Weidner,
preprint arXiv (2023).
Regularity theory for nonlocal obstacle problems with critical and subcritical scaling, pdf
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
preprint arXiv (2023).
Optimal regularity and fine asymptotics for the porous medium equation in bounded domains, pdf
Tianling Jin, Xavier Ros-Oton, Jingang Xiong,
J. Reine Angew. Math. (2024), to appear.
Optimal regularity for the fully nonlinear thin obstacle problem, pdf
Maria Colombo, Xavier Fernandez-Real, Xavier Ros-Oton,
J. Eur. Math. Soc. (2024), to appear.
Optimal regularity for supercritical parabolic obstacle problems, pdf
Xavier Ros-Oton, Clara Torres-Latorre,
Comm. Pure Appl. Math. 77 (2024), 1724-1765.
Global Schauder theory for minimizers of the H^s(\Omega) energy, pdf
Mouhamed Moustapha Fall, Xavier Ros-Oton,
J. Funct. Anal. 283 (2022), 109523, 50pag.
The singular set in the Stefan problem, pdf
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
J. Amer. Math. Soc. 37 (2024), 305-389.
Non-symmetric stable operators: regularity theory and integration by parts, pdf
Serena Dipierro, Xavier Ros-Oton, Joaquim Serra, Enrico Valdinoci,
Adv. Math. 401 (2022), 108321, 100pag.
New boundary Harnack inequalities with right hand side, pdf
Xavier Ros-Oton, Clara Torres-Latorre,
J. Differential Equations 288 (2021), 204-249.
Stable cones in the thin one-phase problem, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Amer. J. Math., in press (2024).
Sharp quantitative stability for isoperimetric inequalities with homogeneous weights, pdf
Eleonora Cinti, Federico Glaudo, Aldo Pratelli, Xavier Ros-Oton, Joaquim Serra,
Trans. Amer. Math. Soc. 375 (2022), 1509-1550.
Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional Laplacian, pdf
Simon Eberle, Xavier Ros-Oton, Georg Weiss,
Nonlinear Anal. 211 (2021), 112473.
Special issue on "Free boundary problems".
The Neumann problem for the fractional Laplacian: regularity up to the boundary, pdf
Alessandro Audrito, Juan-Carlos Felipe-Navarro, Xavier Ros-Oton,
Ann. Sc. Norm. Super. Pisa Cl. Sci. 24 (2023), 1155-1222.
Free boundary regularity for almost every solution to the Signorini problem, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Arch. Rat. Mech. Anal. 240 (2021), 419-466.
Generic regularity of free boundaries for the obstacle problem, pdf
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
Publ. Math. Inst. Hautes Études Sci. 132 (2020), 181-292.
The Dirichlet problem for nonlocal elliptic operators with C^\alpha exterior data, pdf
Alessandro Audrito, Xavier Ros-Oton,
Proc. Amer. Math. Soc. 148 (2020), 4455-4470.
Obstacle problems for integro-differential operators: higher regularity of free boundaries, pdf
Nicola Abatangelo, Xavier Ros-Oton,
Adv. Math. 360 (2020), 106931, 61pp.
Stable solutions to semilinear elliptic equations are smooth up to dimension 9, pdf
Xavier Cabré, Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
Acta Math. 224 (2020), 187-252.
On global solutions to semilinear elliptic equations related to the one-phase free boundary problem, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Discrete Contin. Dyn. Syst. A 39 (2019), 6945-6959.
Special issue Dedicated to Luis Caffarelli on the Occasion of his 70th Birthday.
Higher-order boundary regularity estimates for nonlocal parabolic equations, pdf
Xavier Ros-Oton, Hernan Vivas,
Calc. Var. Partial Differential Equations 57 (2018), 111.
Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian, pdf
Nicola Garofalo, Xavier Ros-Oton,
Rev. Mat. Iberoam. 35 (2019), 1309-1365.
The obstacle problem for the fractional Laplacian with critical drift, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Math. Ann. 371 (2018), 1683-1735.
The boundary Harnack principle for nonlocal elliptic operators in non-divergence form, pdf
Xavier Ros-Oton, Joaquim Serra
Potential Anal. 51 (2019), 315-331.
Free boundary regularity in the parabolic fractional obstacle problem, pdf
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,
Comm. Pure Appl. Math. 71 (2018), 2129-2159.
On the regularity of the free boundary in the p-Laplacian obstacle problem, pdf
Alessio Figalli, Brian Krummel, Xavier Ros-Oton,
J. Differential Equations 263 (2017), 1931-1945.
The structure of the free boundary in the fully nonlinear thin obstacle problem, pdf
Xavier Ros-Oton, Joaquim Serra
Adv. Math. 316 (2017), 710-747.
Obstacle problems for integro-differential operators: regularity of solutions and free boundaries, pdf
Luis Caffarelli, Xavier Ros-Oton, Joaquim Serra
Invent. Math. 208 (2017), 1155-1211.
Boundary regularity estimates for nonlocal elliptic equations in C^1 and C^{1,\alpha} domains, pdf
Xavier Ros-Oton, Joaquim Serra
Ann. Mat. Pura Appl. 196 (2017), 1637-1668.
Regularity theory for general stable operators: parabolic equations, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
J. Funct. Anal. 272 (2017), 4165-4221.
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains, pdf
Matteo Bonforte, Alessio Figalli, Xavier Ros-Oton,
Comm. Pure Appl. Math. 70 (2017), 1472-1508.
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian, pdf
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,
Amer. J. Math. 140 (2018), 415-447.
A one-dimensional symmetry result for a class of nonlocal equations in the plane, pdf
Francois Hamel, Xavier Ros-Oton, Yannick Sire, Enrico Valdinoci,
Ann. Inst. H. Poincare Anal. Non Lineaire 34 (2017), 469-482.
Pohozaev identities for anisotropic integro-differential operators, pdf
Xavier Ros-Oton, Joaquim Serra, Enrico Valdinoci,
Comm. Partial Differential Equations 42 (2017), 1290-1321.
The Dirichlet problem for nonlocal operators with singular kernels: convex and nonconvex domains, pdf
Xavier Ros-Oton, Enrico Valdinoci,
Adv. Math. 288 (2016), 732-790.
Regularity theory for general stable operators, pdf
Xavier Ros-Oton, Joaquim Serra,
J. Differential Equations 260 (2016), 8675-8715.
Boundary regularity for fully nonlinear integro-differential equations, pdf
Xavier Ros-Oton, Joaquim Serra,
Duke Math. J. 165 (2016), 2079-2154.
Nonlocal problems with Neumann boundary conditions, pdf
Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci,
Rev. Mat. Iberoam. 33 (2017), 377-416.
Boundary regularity for the fractional heat equation, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Rev. Acad. Cienc. Ser. A Math. 110 (2016), 49-64.
Local integration by parts and Pohozaev identities for higher order fractional Laplacians, pdf
Xavier Ros-Oton, Joaquim Serra,
Discrete Contin. Dyn. Syst. A 35 (2015), 2131-2150.
Regularity for the fractional Gelfand problem up to dimension 7, pdf
Xavier Ros-Oton,
J. Math. Anal. Appl. 419 (2014), 10-19.
Nonexistence results for nonlocal equations with critical and supercritical nonlinearities, pdf
Xavier Ros-Oton, Joaquim Serra,
Comm. Partial Differential Equations 40 (2015), 115-133.
The extremal solution for the fractional Laplacian, pdf
Xavier Ros-Oton, Joaquim Serra,
Calc. Var. Partial Differential Equations 50 (2014), 723-750.
Sharp isoperimetric inequalities via the ABP method, pdf
Xavier Cabré, Xavier Ros-Oton, Joaquim Serra,
J. Eur. Math. Soc. 18 (2016), 2971-2998.
The Pohozaev identity for the fractional Laplacian, pdf
Xavier Ros-Oton, Joaquim Serra,
Arch. Rat. Mech. Anal. 213 (2014), 587-628.
The Dirichlet problem for the fractional Laplacian: regularity up to the boundary, pdf
Xavier Ros-Oton, Joaquim Serra,
J. Math. Pures Appl. 101 (2014), 275-302.
Sobolev and isoperimetric inequalities with monomial weights, pdf
Xavier Cabré, Xavier Ros-Oton,
J. Differential Equations 255 (2013), 4312-4336.
Regularity of stable solutions up to dimension 7 in domains of double revolution, pdf
Xavier Cabré, Xavier Ros-Oton,
Comm. Partial Differential Equations 38 (2013), 135-154.
Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations, pdf
Josep M. Olm, Xavier Ros-Oton,
Discrete Contin. Dyn. Syst. A 33 (2013), 1603-1614.
On a factorization of Riemann's zeta function with respect to a quadratic field and its computation, pdf
Xavier Ros-Oton,
Rev. Acad. Cienc. Ser. A Math. 106 (2012), 419-427.
Periodic solutions with nonconstant sign in Abel equations of second kind, pdf
Josep M. Olm, Xavier Ros-Oton, Tere M. Seara,
J. Math. Anal. Appl. 381 (2011), 582-589.
Stable inversion of Abel equations: application to tracking control in DC-DC nonminimum phase boost converters, pdf
Josep M. Olm, Xavier Ros-Oton, Yuri B. Shtessel,
Automatica J. IFAC 47 (2011), 221-226.
Approximate tracking of periodic references in a class of bilinear systems via stable inversion, pdf
Josep M. Olm, Xavier Ros-Oton,
Discrete Contin. Dyn. Syst. Ser. B 15 (2011), 197-215.
Mirando hacia el futuro: problemas de frontera libre, pdf
Xavier Ros-Oton,
La Gaceta de la RSME 24 (2021), 399-416.
Regularitat i singularitats en problemes de frontera lliure, pdf
Xavier Ros-Oton, Joaquim Serra,
Butlletí de la Societat Catalana de Matemàtiques 35 (2020), 155-176.
Understanding singularities in free boundary problems, pdf
Xavier Ros-Oton, Joaquim Serra,
Matematica, Cultura e Societa 4 (2019), 107-118.
Special volume in honor of Alessio Figalli.
Obstacle problems and free boundaries: an overview, pdf
Xavier Ros-Oton,
SeMA J. 75 (2018), 399-419.
Boundary regularity, Pohozaev identities, and nonexistence results, pdf
Xavier Ros-Oton,
Chapter 9 in the book Recent developments in the Nonlocal Theory, De Gruyter, 2018.
Nonlocal elliptic equations in bounded domains: a survey, pdf
Xavier Ros-Oton,
Publ. Mat. 60 (2016), 3-26.
Euclidean balls solve some isoperimetric problems with nonradial weights, pdf
Xavier Cabré, Xavier Ros-Oton, Joaquim Serra,
C. R. Math. Acad. Sci. Paris 350 (2012), 945-947.
Fractional Laplacian: Pohozaev identity and nonexistence results, pdf
Xavier Ros-Oton, Joaquim Serra,
C. R. Math. Acad. Sci. Paris 350 (2012), 505-508.