Felipe Perez Silva

Felipe Perez Silva

PhD student at George Mason University.

Publications

Submitted

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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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.

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.

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.

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.