Home / Faculty / Avila, Jake

Avila, Jake

Assistant Professor
Email Addressjavila@math.upd.edu.ph
RoomMath Building 258
Research Interests
Partial differential equations: homogenization theory, spectral theory, variational inequalities
Academic Groups
  • Education
    • Doctor of Philosophy in Mathematics (2024)
      University of the Philippines Diliman (with dissertation at University of Salerno, Italy)

      Dissertation: Homogenization of Elliptic Boundary Value Problems in Two-component Domains
      Adviser: Bituin Cabarrubias, Ph.D. and Prof. Sara Monsurrò (University of Salerno, Italy)

    • Master of Science in Mathematics (2019)
      University of the Philippines Diliman

      Thesis: Homogenization of Some Boundary Value Problems in Perforated Domains
      Adviser: Bituin Cabarrubias, Ph.D.

    • Bachelor of Science in Mathematics (2017), Cum laude, Leticia Shahani Award for Best Undergraduate Thesis
      University of the Philippines Diliman

      Thesis: On Homogenization of an Optimal Control Problem in a Fixed Domain with a Robin Boundary Condition
      Adviser: Bituin Cabarrubias, Ph.D.

  • Research

    Professional Profiles

  • Teaching

    Second Semester Academic Year 2025 – 2026

    • Math 10 (Math, Culture and Society) WFX: WF 1:00 – 2:30 pm
    • Math 123.1 (Advanced Calculus I) WFW-2: WF 2:30 – 4:00 pm

     

    Past general education courses handled

    • Math 10 (Math, Culture and Society)

     

    Past undergraduate courses handled

    • Math 20 (Precalculus)
    • Math 21 (Elementary Analysis I)
    • Math 22 (Elementary Analysis II)
    • Math 100 (Introduction to Calculus)
    • Math 123.1 (Advanced Calculus I)

     

    Past graduate courses handled

    • Math 221 (Partial Differential Equations)

     

     

  • Publications

    Peer-reviewed Articles

    1. Avila, J.: Homogenization and corrector results of elliptic problems with Signorini boundary conditions in perforated domains. Annali di Matematica Pura ed Applicata (2024).
      https://doi.org/10.1007/s10231-024-01510-7
    2. Avila, J.: Homogenization of quasilinear problems with semilinear terms and Signorini boundary conditions in perforated domains. Nonlinear Differential Equations and Applications 31, no.64 (2024).
      https://doi.org/10.1007/s00030-024-00957-0

    3. Avila, J., Monsurrò, S., Raimondi, F.: Homogenization of an eigenvalue problem through rough surfaces. Asymptotic Analysis 137, no.1–2, 97–121 (2024).
      https://doi.org/10.3233/ASY-231882

    4. Avila, J., Cabarrubias, B.: Asymptotic behavior of a quasilinear problem with Neumann boundary condition in domains with small holes. Matimyás Matematika 47, no.1, 1–20 (2024)

    5. Avila, J., Cabarrubias, B.: Periodic unfolding method for domains with very small inclusions. Electronic Journal of Differential Equations 2023, no.85, 1–37 (2023).
      https://doi.org/10.58997/ejde.2023.85

    6. Avila, J., Cabarrubias, B.: Homogenization of a quasilinear elliptic problem in domains with small holes. Applicable Analysis 101, no.15, 5193–5212 (2021).
      https://doi.org/10.1080/00036811.2021.1884226

     

    Conference Proceedings

    1. Avila, J., Cabarrubias, B.: Homogenization of an optimal control problem in fixed domains. Proceedings of the World Congress on Engineering 2017. Lecture Notes in Engineering and Computer Science 2229, 143–147 (2017)