Posts by Collection

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.
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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.

Seminar on Nonlinear Analysis of Partial Differential Equations

Published: April 01, 2021

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: February 01, 2025

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: March 01, 2025

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: April 01, 2025

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: June 01, 2025

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: February 01, 2026

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.

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.