Avila, Jake
Partial differential equations: homogenization theory, spectral theory, variational inequalities
- Differential Equations (member)
- Modelling and Applications (affiliate)
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Education
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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 DilimanThesis: 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 DilimanThesis: On Homogenization of an Optimal Control Problem in a Fixed Domain with a Robin Boundary Condition
Adviser: Bituin Cabarrubias, Ph.D.
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Doctor of Philosophy in Mathematics (2024)
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Research
Professional Profiles
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Publications
Peer-reviewed Articles
- 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 - 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 -
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 -
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)
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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 - 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
- Avila, J., Cabarrubias, B.: Homogenization of an optimal control problem in fixed domains.
- Avila, J.: Homogenization and corrector results of elliptic problems with Signorini boundary conditions in perforated domains. Annali di Matematica Pura ed Applicata (2024).