Sitemap
A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.
Pages
Posts
Future Blog Post
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Blog Post number 4
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 3
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 2
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 1
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
publications
Existence and Multiplicity of Positive Solutions for a Quasilinear Problem with Nonhomogeneous Dirichlet Condition
Published in Preprint (submitted), 2025
We study existence and multiplicity of positive solutions for a quasilinear elliptic problem involving the p-Laplacian under nonhomogeneous Dirichlet boundary conditions, using variational and sub/super-solution methods.
Recommended citation: L. Iturriaga and F. Pérez. (2025). "Existence and Multiplicity of Positive Solutions for a Quasilinear Problem with Nonhomogeneous Dirichlet Condition." Preprint.
Optimal Boundary Control of Diffusion on Graphs via Linear Programming
Published in Preprint (submitted), 2025
A linear programming framework for steady-state diffusion and flux optimization on geometric networks. Boundary potentials act as controls; we prove existence of optimal solutions and identify sufficient boundedness conditions, with numerical experiments on real-world networks.
Recommended citation: H. Antil, R. Löhner, and F. Pérez. (2025). "Optimal Boundary Control of Diffusion on Graphs via Linear Programming." Preprint. arXiv:2511.03129.
Download Paper
Convex Duality and Guaranteed A Posteriori Error Control for Curl–Curl Maxwell Problems with Pointwise Field Bounds
Published in In preparation, 2026
A convex-duality framework for curl–curl Maxwell problems subject to pointwise field bounds, with guaranteed a posteriori error estimates and supporting numerics.
Recommended citation: H. Antil, A. Kaltenbach, F. Pérez, T. Prieto, and V. Lagos. (2026). "Convex Duality and Guaranteed A Posteriori Error Control for Curl–Curl Maxwell Problems with Pointwise Field Bounds." In preparation.
Duality Framework for the Double Obstacle Problem: Analysis and Numerics
Published in In preparation, 2026
A duality-based approach to the double obstacle problem, covering analytical aspects and a numerical scheme with supporting experiments.
Recommended citation: H. Antil and F. Pérez. (2026). "Duality Framework for the Double Obstacle Problem: Analysis and Numerics." In preparation.
Duality Framework for Flux Constrained Flow: Analysis and Numerics
Published in In preparation, 2026
A duality framework for flow problems with flux constraints, addressing both the analytical foundations and the numerical realization via finite elements.
Recommended citation: H. Antil, K. L. A. Kirk, and F. Pérez. (2026). "Duality Framework for Flux Constrained Flow: Analysis and Numerics." In preparation.
talks
Seminar on Nonlinear Analysis of Partial Differential Equations
Published:
A semester-long doctoral working seminar on nonlinear analysis of partial differential equations, in which I participated as a regular presenter. My talks introduced techniques for proving existence of solutions to nonlinear PDEs, including minimax theorems (the Mountain Pass Theorem and the Linking Theorem) and the supporting machinery: the Nemytskii operator, the Deformation Lemma, and Palais–Smale-type compactness conditions.
Seminar on Control of Partial Differential Equations
Published:
A semester-long working seminar on the control of partial differential equations, in which I participated as a regular presenter alongside my advisor’s research group. My contributions focused on the Fenchel conjugate and the construction of primal and dual problems for PDE-constrained optimization, illustrating the convex-duality machinery underlying our current research on a post
Seminar on Calculus of Variations
Published:
Invited talk at the Georgetown University Seminar on Calculus of Variations. I discussed convex-duality techniques in the calculus of variations and their role in our recent work on constrained PDE problems and a posteriori error analysis.
Duality Framework for Flux Constrained Flow: Analysis and Numerics
Published:
Talk delivered at the Finite Element Circus hosted at George Mason University. I presented a convex-duality framework for flow problems subject to flux constraints, covering both the analytical foundations and the numerical realization through finite element discretization. The talk drew on joint work with H. Antil and K. L. A. Kirk.
Optimal Control and Decision Making Under Uncertainty for Digital Twins
Published:
Poster presentation at the IMSI workshop Optimal Control and Decision Making Under Uncertainty for Digital Twins. The poster summarized our work on convex-duality methods and a posteriori error estimates for constrained PDE problems. I presented a convex-duality framework for flow problems subject to flux constraints, covering both the analytical foundations and the numerical realization through finite element discretization. The talk drew on joint work with H. Antil and K. L. A. Kirk.
Simulation-Based Optimization with Applications
Published:
Poster presentation at the ICERM workshop Simulation-Based Optimization with Applications. The poster presented our convex-duality framework for flow problems subject to flux constraints, covering both the analytical foundations and the numerical realization through finite element discretization. The talk drew on joint work with H. Antil and K. L. A. Kirk.
teaching
MAT021 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2018
Teaching Assistant for MAT021 — Mathematics I. Responsibilities included leading problem sessions and grading homework and exams.
MAT021 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2018
Teaching Assistant for MAT021 — Mathematics I. Responsibilities included leading problem sessions and grading homework and exams.
MAT060 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2019
Teaching Assistant for MAT060 — Algebra and Analytic Geometry. Responsibilities included leading problem sessions and grading homework and exams.
MAT060 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2019
Teaching Assistant for MAT060 — Algebra and Analytic Geometry. Responsibilities included leading problem sessions and grading homework and exams.
MAT060 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2020
Teaching Assistant for MAT060 — Algebra and Analytic Geometry. Responsibilities included leading problem sessions and grading homework and exams.
MAT061 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2020
Teaching Assistant for MAT061 — Linear Algebra. Responsibilities included leading problem sessions and grading homework and exams.
MAT021 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2021
Teaching Assistant for MAT021 — Mathematics I. Responsibilities included leading problem sessions and grading homework and exams.
MAT021 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2022
Teaching Assistant for MAT021 — Mathematics I. Responsibilities included leading problem sessions and grading homework and exams.
MAT247 — USM
Teaching Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2022
Teaching Assistant for MAT247 — Partial Differential Equations. Responsibilities included leading problem sessions and grading homework and exams.
MAT021 — USM
Laboratory Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2023
Laboratory Assistant for MAT021 — Mathematics I. Responsibilities consisted of authoring original problems and worked solutions in differential calculus, uploading them to the department’s online platform, and scheduling the quizzes. The platform served all sections of MAT021 across the university, giving students problems to prepare for examinations and providing instructors with current data on cohort performance.
MAT021 — USM
Laboratory Assistant, Universidad Técnica Federico Santa María, Department of Mathematics, 2023
Laboratory Assistant for MAT021 — Mathematics I. Responsibilities consisted of authoring original problems and worked solutions in differential calculus, uploading them to the department’s online platform, and scheduling the quizzes. The platform served all sections of MAT021 across the university, giving students problems to prepare for examinations and providing instructors with current data on cohort performance.
MAT012, MAT021, and MAT022 — USM
Term Professor (Instructor of Record), Universidad Técnica Federico Santa María, Department of Mathematics, 2024
Term Professor (sole instructor) at Universidad Técnica Federico Santa María. Full responsibility for the three courses below: lectures, problem sessions, assessment design, exam writing and grading, office hours, and final grade assignment.
Calculus I and II
Graduate Teaching Assistant, George Mason University, Department of Mathematical Sciences, 2024
Graduate Teaching Assistant for Calculus I and Calculus II at George Mason University. Responsibilities included leading recitation sections, holding weekly office hours, grading exams and assignments, and answering student questions on the underlying theory and computational techniques.