G. Acosta, E. Belén, F.M. Bersetche, J.P. Borthagaray. A deep first-order system least squares method for the obstacle problem. 2025.
J.P. Borthagaray, P. Ciarlet Jr. On some coupled local and nonlocal diffusion models. 2025.
J.P. Borthagaray, N. de León. A mixed formulation for the fractional Poisson problem. 2025.
J.P. Borthagaray, R.H. Nochetto, A.J. Salgado, C. Torres. Monotone two-scale methods for a class of integrodifferential operators and applications. To appear in Interfaces and Free Boundaries.
J.P. Borthagaray, W. Li, R.H. Nochetto. Quasi-linear fractional-order operators in Lipschitz domains. SIAM Journal on Mathematical Analysis, 56(3):4006–4039, 2024.
J.P. Borthagaray, R.H. Nochetto. Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains. Journal of Functional Analysis, 284(6):109829, 2023.
J.P. Borthagaray, R.H. Nochetto, S. Wu, J. Xu. Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains. Mathematics of Computation, 92:2439–2473, 2023.
F.M. Bersetche, J.P. Borthagaray. A deep first-order system least squares method for solving elliptic PDEs. Computers and Mathematics with Applications, 129(1): 136–150, 2023.
J.P. Borthagaray, R.H. Nochetto. Constructive approximation on graded meshes for the integral fractional Laplacian. Constructive Approximation, 57:463–487, 2023.
F.M. Bersetche, J.P. Borthagaray. Finite element approximation of fractional Neumann problems. IMA Journal on Numerical Analysis, 42(4):3207--3240, 2022.
J.P. Borthagaray, W. Li, R.H. Nochetto. Finite element algorithms for nonlocal minimal graphs. Mathematics in Engineering, 4(2):1–29, 2021.
J.P. Borthagaray, D. Leykekhman, R.H. Nochetto. Local energy estimates for the fractional Laplacian. SIAM Journal on Numerical Analysis, 59(4):1918–1947, 2021.
J.P. Borthagaray, S.W. Walker. The Q-tensor model with uniaxial constraint. Handbook of Numerical Analysis, 22:313–382, 2021.
J.P. Borthagaray, R.H. Nochetto, S.W. Walker. A structure-preserving FEM for the uniaxially constrained Q-tensor model of nematic liquid crystals. Numerische Mathematik, 145:837–881, 2020.
J.P. Borthagaray, R.H. Nochetto, A.J. Salgado. Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Mathematical Models and Methods in Applied Sciences, 29(14):2679–2717, 2019.
J.P. Borthagaray, W. Li, R.H. Nochetto. Finite element discretizations for graph nonlocal minimal surfaces: convergence. Nonlinear Analysis, 189:111566, 2019.
J.P Borthagaray, P. Ciarlet Jr. On the convergence in H^1-norm for the fractional Laplacian. SIAM Journal on Numerical Analysis, 57(4):1723–1743, 2019.
G. Acosta, F.M. Bersetche, J.P. Borthagaray. Finite element approximations for fractional evolution problems. Fractional Calculus and Applied Analysis, 22(3):767–794, 2019.
G. Acosta, J.P. Borthagaray, N. Heuer. Finite element approximations of the non-homogeneous fractional Dirichlet problem. IMA Journal on Numerical Analysis, 29(3):1471– 1501, 2019.
J.P. Borthagaray, L.M. Del Pezzo, S. Martínez. Finite element approximation for the fractional eigenvalue problem. Journal of Scientific Computing, 77(1):308–329, 2018.
A. Bonito, J.P. Borthagaray, R.H. Nochetto, E. Otárola, A.J. Salgado. Numerical methods for fractional diffusion. Computing and Visualization in Science, 19(5– 6):19–46, 2018.
G. Acosta, J.P. Borthagaray, O. Bruno, M. Maas. Regularity theory and high order numerical methods for the (1d)-Fractional Laplacian. Mathematics of Computation, 87(312):1821–1857, 2018.
G. Acosta, F.M. Bersetche, J.P. Borthagaray. A short FE implementation for a 2D homogeneous Dirichlet problem of a fractional Laplacian. Computers and Mathematics with Applications, 74(4):784–816, 2017.
G. Acosta, J.P. Borthagaray. A fractional Laplace equation: regularity of solutions and finite element approximations. SIAM Journal on Numerical Analysis, 55(2):472–495, 2017.
J.P. Borthagaray, J. Fernández Bonder, A. Silva. A mass transportation approach for Sobolev inequalities in variable exponent spaces. Manuscripta Mathematica, 151(1):133–146, 2016.
J.P. Borthagaray, W. Li, R.H. Nochetto. Fractional elliptic problems on Lipschitz domains: regularity and approximation. A^3N^2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models, 27–99. Springer, 2023.
J.P. Borthagaray, W. Li, R.H. Nochetto. Linear and nonlinear fractional elliptic problems. In 75 Years of Mathematics of Computation, Contemporary Mathematics, 754:69–92. American Mathematical Society, Providence, 2020.
F.M. Bersetche, J.P. Borthagaray. A deep first-order system least squares method for solving elliptic PDEs. In VIII Congreso De Matemática Aplicada, Computacional e Industrial, pp. 87–90, 2021.
F.M. Bersetche, J.P. Borthagaray. Finite element approximation of fractional Neumann problems. In VIII Congreso De Matemática Aplicada, Computacional e Industrial, pp. 47–50, 2021.
J.P. Borthagaray, P. Ciarlet, Jr. Nonlocal models for interface problems between dielectrics and metamaterials. In 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena, pp. 61–63, 2017.
G. Acosta, F.M. Bersetche, J.P. Borthagaray. A finite element method for fractional evolution problems. In VI Congreso De Matemática Aplicada, Computacional e Industrial, pp. 145–148, 2017.
G. Acosta, J.P. Borthagaray, A. Lombardi. Isogeometric analysis in exterior cusps. In IV Congreso De Matemática Aplicada, Computacional e Industrial, pp. 219–222, 2013.