Alejandro Vélez-Santiago

            Associate Professor of Mathematics            

            Department of Mathematical Sciences
            University of Puerto Rico at Mayagüez (UPRM)

            Call Box 9000
            Mayagüez, PR 00681

            Office: CH 508D
            E-mail:  alejandro.velez2@upr.edu

           Other Online Pages:  Webpage UPRM;  Math Alliance;  ResearchGate;  LinkedIn;  Facebook;  ORCID;  Google Scholar;  Lathisms

      Work Experience:


Courses Teaching

    Present University (UPRM)

    Past Universities

       Education:

         Research Interests:

        Research Grants:

            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

        Publications:

            1) Books:

·         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.

·         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.

·         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.

·         L. F. Cáceres, O. Colón, B. Morales*, A. Portnoy, A. Vélez-Santiago, OMPR Olimpiadas Matemáticas de Puerto Rico 2018-2019, OMPR, UPRM, 2019.

·         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.

·         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.

            2) Research Papers:

·         M. R. Lancia, A. Vélez-Santiago, A priori estimates for general elliptic and parabolic boundary value problems over irregular domains, Submitted.

·         G. Ferrer*, A. Vélez-Santiago, 3D Koch-type crystals, J. Fractal Geometry  (to appear).

·         C. Carvajal-Ariza*, J. Henríquez-Amador*, A. Vélez-Santiago, The generalized anisotropic dynamical Wentzell heat equation with nonstandard growth conditions, J. d'Analyse Mathématique  (to appear).

·         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).

·         M.-M. Boureanu, A. Vélez-Santiago, Applied higher-order elliptic problems with nonstandard growth structure, Applied Mathematics Letters 123 (2022), 107603 (7 pages).

·         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).

·         K. Ríos-Soto, C. Seda-Damiani**, A. Vélez-Santiago, The variable exponent Bernoulli differential equation, Involve, a Journal of Mathematics 12 (2019), 1279—1291.

·         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.

·         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. 

·         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.

·         A. Vélez-Santiago, A quasi-linear Neumann problem of Ambrosetti—Prodi type on extension domains, Nonlinear Analysis: Theory, Methods & Applications 160 (2017), 191—210.

·         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.

·         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.

·         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.

·         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.

·         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.

·         A. Vélez-Santiago, Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions,  J. Functional Analysis 266 (2014), 560—615.

·         A. Vélez-Santiago, Solvability of linear local and nonlocal Robin problems over C(Ω), J. Mathematical Analysis and Applications 386 (2012), 677—698.

·         A. Vélez-Santiago, Quasi-linear boundary value problems with generalized nonlocal boundary conditions, Nonlinear Analysis: Theory, Methods & Applications 74 (2011), 4601—4621.

·         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.

                                
                                * = Graduate Student;   ** = Undergraduate Student

          Organizations:


        Other Activities:

         * I am currently working in the project: Olimpiadas de Matemáticas en Puerto Rico (OMPR).   
       
        *  I was featured in the Lathisms calendar for the year 2022; you can read my short biography here.
           
           * I am a professional violinist.  I have played in the Central Iowa symphony, and in the Puerto Rico symphony orchestra, among many other orchestras and groups.