University of Puerto Rico    (787) 764 0000

    Professor Information

    Alejandro Vélez-Santiago

    Address Department of Mathematics, 17 University Ave. Ste 1701
    San Juan PR, 00925-2537
    Office NCN II C-112
    Hours
    Actual Program
    Telephone (787) 764-0000 88277
    E-Mail ude.rpu@2zelev.ordnajela

    Education

    PhD, University of Puerto Rico, Rio Piedras, 2010

    Research Interests

    Elliptic and parabolic boundary value problems on non-smooth domains, Generation of operator semigroups, Potential theory, Analysis on fractals, Operator theory and Functional Analysis.

    Selected Publications

    Books:

    1. L. F. Cáceres, O. Colón, J. Flores*, D. Gutiérrez*, F. Henao*, J. Jiménez*, S. López*, J. Ortega*, A. Portnoy, A. Vélez-Santiago, OMPR Olimpiadas Matemáticas de Puerto Rico 2021-2022, OMPR, UPRM, 2023.
    2. L. F. Cáceres, O. Colón, D. Gutiérrez*, F. Henao*, J. Jiménez*, S. López*, J. Ortega*, B. Morales*, A. Portnoy, A. Vélez-Santiago, OMPR Olimpiadas Matemáticas de Puerto Rico 2020-2021, OMPR, UPRM, 2022.
    3. L. F. Cáceres, O. Colón, D. Gutiérrez*, B. Morales*, A. Portnoy, A. Vélez-Santiago, OMPR Olimpiadas Matemáticas de Puerto Rico 2019-2020, OMPR, UPRM, 2021.
    4. L. F. Cáceres, O. Colón, B. Morales*, A. Portnoy, A. Vélez-Santiago, OMPR Olimpiadas Matemáticas de Puerto Rico 2018-2019, OMPR, UPRM, 2019.
    5. L. F. Cáceres, O. Colón, B. Morales*, A. Portnoy, P. A. Torres, A. Vélez-Santiago, OMPR Olimpiadas Matemáticas de Puerto Rico 2017-2018, Publicaciones AFAMaC, 2018.
    6. L. F. Cáceres, O. Colón, A. Portnoy, P. A. Torres, A. Vélez-Santiago, M. Zepeda, OMPR Olimpiadas Matemáticas de Puerto Rico 2016-2017, Publicaciones AFAMaC, 2017.

    Research Papers:

    1. K. Silva-Pérez*, A. Vélez-Santiago, Diffusion over ramified domains: solvability and fine regularity, Submitted.
    2. M. R. Lancia, A. Vélez-Santiago, A priori estimates for general elliptic and parabolic boundary value problems over irregular domains, Submitted.
    3. G. Ferrer*, A. Vélez-Santiago, 3D Koch-type crystals, J. Fractal Geometry  10 (2023), 109—149.
    4. C. Carvajal-Ariza*, J. Henríquez-Amador*, A. Vélez-Santiago, The generalized anisotropic dynamical Wentzell heat equation with nonstandard growth conditions, J. d'Analyse Mathématique  (2023) [in press].
    5. V. Díaz-Martínez*, A. Vélez-Santiago, Generalized anisotropic elliptic Wentzell problems with nonstandard growth conditions, Nonlinear Analysis: Real World Applications 68 (2022), 103689 (44 pages).
    6. M.-M. Boureanu, A. Vélez-Santiago, Applied higher-order elliptic problems with nonstandard growth structure, Applied Mathematics Letters 123 (2022), 107603 (7 pages).
    7. J. Henríquez-Amador*, A. Vélez-Santiago, Generalized anisotropic Neumann problems of Ambrosetti—Prodi type with nonstandard growth conditions, J. Mathematical Analysis and Applications 494 (2021), 124668 (38 pages).
    8. K. Ríos-Soto, C. Seda-Damiani**, A. Vélez-Santiago, The variable exponent Bernoulli differential equation, Involve, a Journal of Mathematics 12 (2019), 1279—1291.
    9. M. R. Lancia, A. Vélez-Santiago, P. Vernole, A quasi-linear nonlocal Venttsel' problem of Ambrosetti--Prodi type on fractal domains, Discrete & Continuous Dynamical Systems - Series A 39 (2019), 4487—4518.
    10. M.-M. Boureanu, A. Vélez-Santiago, Fine regularity for elliptic and parabolic anisotropic Robin problems with variable exponents, J. Differential Equations 266 (2019), 8164—8232. 
    11. S. Creo,  M. R. Lancia,  A. Vélez-Santiago,  P. Vernole, Approximation of a nonlinear fractal energy functional on varying Hilbert spaces, Communications on Pure and Applied Analysis 17 (2018), 647—669.
    12. A. Vélez-Santiago, A quasi-linear Neumann problem of Ambrosetti—Prodi type on extension domains, Nonlinear Analysis: Theory, Methods & Applications 160 (2017), 191—210.
    13. M. R. Lancia,  A. Vélez-Santiago,  P. Vernole, Quasi-linear Venttsel' problems with nonlocal boundary conditions on fractal domains, Nonlinear Analysis: Real World Applications 35 (2017), 265—291.
    14. A. Vélez-Santiago, Embedding and trace results for variable exponent Sobolev and Maz'ya spaces on non-smooth domains, Glasgow Mathematical J. 58 (2016), 471—489.
    15. A. Vélez-Santiago, Ambrosetti—Prodi-type problems for quasi-linear elliptic equations with nonlocal boundary conditions, Calculus of Variations and Partial Differential Equations 54 (2015), 3439—3469.
    16. A. Vélez-Santiago, Global regularity for a class of quasi-linear local and nonlocal elliptic equations on extension domains, J. Functional Analysis 269 (2015), 1—46.
    17. A. Vélez-Santiago, On the well-posedness of first order variable exponent Cauchy problems with Robin and Wentzell-Robin boundary conditions on arbitrary domains, J. Abstract Differential Equations and Applications 6 (2015), 1—20.
    18. A. Vélez-Santiago, Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions,  J. Functional Analysis 266 (2014), 560—615.
    19. A. Vélez-Santiago, Solvability of linear local and nonlocal Robin problems over C(Ω), J. Mathematical Analysis and Applications 386 (2012), 677—698.
    20. A. Vélez-Santiago, Quasi-linear boundary value problems with generalized nonlocal boundary conditions, Nonlinear Analysis: Theory, Methods & Applications 74 (2011), 4601—4621.
    21. A. Vélez-Santiago,  M. Warma, A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions,  J. Mathematical Analysis and Applications 372 (2010), 120—139.

    Grants and Awards

    1. Agency:  Puerto Rico Science, Technology & Research Trust (agreement #: 2022-00014),
      Project:  Boundary value problems of nonstandard growth structure over real world regions,
      Amount: $150,000,
      Period: July 2021 - July 2023

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