R. H. Bing Instructor
Department of Mathematics, RLM 11.108
2515 Speedway, Austin, TX 78712, USA
email: ros.oton at math.utexas.edu
Research Statement (October 2016)
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
Submitted, available at arXiv.
Regularity theory for general stable operators: parabolic equations, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Submitted, available at arXiv.
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, to appear.
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., to appear.
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, 2016.
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 DMS-1565186 (July 2016 -- June 2019)
Premio Vicent Caselles 2015 from the Real Sociedad Matemática Española (young researcher award)
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
First Prize at Cangur 2005 and 2006 (catalan version of the Mathematical Kangaroo)