Published in Preprint (submitted), 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." Preprint. arXiv:2607.13256.
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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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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.