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Avila, Jake


Research Interests
Partial differential equations: homogenization theory, spectral theory, variational inequalities
Academic Groups
  • Education
    • Doctor of Philosophy in Mathematics, (ongoing)
      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 C. 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
  • Publications

    Peer-reviewed Articles

    1. Avila, J.: Homogenization of quasilinear problems with semilinear terms and Signorini boundary conditions in perforated domains. Nonlinear Differential Equations and Application NoDEA 31, no.64 (2024). https://doi.org/10.1007/s00030-024-00957-0
    2. Avila, J., Monsurrò, S., Raimondi, F.: Homogenization of an eigenvalue problem through rough surfaces. Asymptotic Analysis 137, no.12, 97121 (2024). https://doi.org/10.3233/ASY-231882

    3. Avila, J., Cabarrubias, B.: Asymptotic behavior of a quasilinear problem with Neumann boundary condition in domains with small holes. Matimyás Matematika 47, no.1, 120 (2024)

    4. Avila, J., Cabarrubias, B.: Periodic unfolding method for domains with very small inclusions. Electronic Journal of Differential Equations 2023, no.85, 137 (2023). https://doi.org/10.58997/ejde.2023.85

    5. Avila, J., Cabarrubias, B.: Homogenization of a quasilinear elliptic problem in domains with small holes. Applicable Analysis 101, no.15, 51935212 (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)