R. H. Bing Instructor
Department of Mathematics, RLM 11.108
2515 Speedway, Austin, TX 78712, USA
email: ros.oton at math.utexas.edu
On the regularity of the free boundary in the p-Laplacian obstacle problem, pdf
Alessio Figalli, Brian Krummel, Xavier Ros-Oton,
J. Differential Equations, to appear.
The obstacle problem for the fractional Laplacian with critical drift, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Submitted, available at arXiv.
The boundary Harnack principle for nonlocal elliptic operators in non-divergence form, pdf
Xavier Ros-Oton, Joaquim Serra
Submitted, available at arXiv.
Free boundary regularity in the parabolic fractional obstacle problem, pdf
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,
Submitted, available at arXiv.
The structure of the free boundary in the fully nonlinear thin obstacle problem, pdf
Xavier Ros-Oton, Joaquim Serra
Submitted, available at arXiv.
Obstacle problems for integro-differential operators: regularity of solutions and free boundaries, pdf
Luis Caffarelli, Xavier Ros-Oton, Joaquim Serra
Invent. Math., to appear.
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., to appear.
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., to appear.
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian, pdf
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,
Submitted, available at arXiv.
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,
Submitted, available at arXiv.
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.
Boundary regularity, Pohozaev identities, and nonexistence results, pdf
Xavier Ros-Oton,
To be published as a Chapter in the book 'Recent developments in the Nonlocal Theory', De Gruyter, 2017.
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.
NSF Analysis Grant, 2016
PI: Xavier Ros-Oton
Awarded amount: $103,617Premio Vicent Caselles 2015 from the Real Sociedad Matemática Española
Extraordinary PhD Prize from the Universitat Politecnica de Catalunya
Premi Évariste Galois 2012 for the Master's Thesis 'Minimizers to reaction-diffusion PDEs, Sobolev inequalities, and monomial weights'
FPU Fellowship from the Ministerio de Educación y Ciencia 2011-2014. Number 1 in the area of Mathematics.
Participant at the X Programa de Jóvenes Líderes Iberoamericanos of the Fundación Carolina, 2011
This program selects the 5 best graduates of the year from each iberoamerican country, and during 3 weeks it provides better knowledge of the European reality to the participants by visiting the main institutions in Brussels, The Hague, and Madrid. Fundación Carolina is a publico-private foundation whose Honorific President is King Juan Carlos I of Spain.
Silver Medals at the International Mathematical Competition for university students 2007, 2008, and 2009
Bronze Medal at the International Mathematical Olympiad 2006
Gold Medal at the Olimpiada Matemática Española 2006