Research interests: My research interests lie primarily in the calculus of variations, partial differential equations, mathematical physics, and geometric analysis.
Email: carlos.roman (at) uc.cl
Publications in Refereed Journals
- (with T. Ried) Domain branching in micromagnetism: scaling law for the global and local energies, Rev. Mat. Iberoam. (2024), published online first.
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- (with E. Sandier and S. Serfaty) Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem, Proc. Lond. Math. Soc. (3) 126 (2023), no. 3, 1015−1062.
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- (with D. Bonheure and J.-B. Casteras) Unbounded mass radial solutions for the Keller-Segel equation in the disk, Calc. Var. Partial Differential Equations 60 (2021), no. 5.
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- On the first critical field in the three dimensional Ginzburg-Landau model of superconductivity, Comm. Math. Phys. 367 (2019), no. 1, 317−349.
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- Three dimensional vortex approximation construction and ε-level estimates for the Ginzburg-Landau functional, Arch. Ration. Mech. Anal. 231 (2019), no. 3, 1531−1614.
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- (with M. del Pino, M. Musso, and J. Wei) Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3, J. Anal. Math. 137 (2019), no. 2, 813−843.
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- (with A. Pistoia) Large conformal metrics with prescribed scalar curvature, J. Differential Equations 263 (2017), no. 9, 5902−5938.
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- (with M. del Pino) Large conformal metrics with prescribed sign-changing Gauss curvature, Calc. Var. Partial Differential Equations 54 (2015), no. 1, 763−789.
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Preprints
- (with M. Díaz-Vera) On the Meissner state for type-II inhomogeneous superconductors.
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- (with P. Bella) Wrinkling of an elastic sheet floating on a liquid sphere.
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