Juan Carlos Sampedro Pascual
Department of Applied Mathematics and Mathematical Analysis
School of Mathematical Sciences
Complutense University of Madrid
Nonlinear Elliptic and Parabolic Equations UCM-GR17-970846
I obtained my PhD in Mathematics at Complutense University of Madrid under the supervision of Professor Julián López-Gómez. During my PhD, I have been supported by the Eusko Jaurlaritza (Basque Government) Predoctoral Fellowship. Funded by its mobility grant and by the national research project PGC2018-097104-B-I00, I carried out three research stays at the Universit'a degli Studi di Udine, the Politecnico di Torino and the University of Swansea. I am currently part of the national research project PID2021-123343NB-I00: Heterogeneous Differential Equations: Dynamics and Numerics.
My research interests are divided into two themes. In the field of Nonlinear Analysis, I focus on Topological Degree Theory, Bifurcation Theory, Nonlinear Spectral Theory and its applications to Nonlinear Elliptic and Parabolic Partial Differential Equations. On the other hand, in the field of Real and Harmonic Analysis, I specialize in Measures in Infinite Dimensional Spaces, Wiener measures on Riemannian Manifolds and Path Integrals and their connections with Quantum Field Theory.
My research focuses on the following topics: Topological degree and Nonlinear Functional Analysis, Nonlinear Spectral Theory, Foundational Real Analysis, Infinite Dimensional Integration and Feynman Integral.
- J. L. Gómez, J. C. Sampedro. Generating loops and isolas in semilinear elliptic BVP's. Nonlinear Analysis, volumen 232, 2023, 113268, ISSN 0362-546X. https://doi.org/10.1016/j.na.2023.113268
- J. C. Sampedro. Approximation Schemes for Path Integration on Riemannian Manifolds. Journal of Mathematical Analysis and Applications. 2022, 512, 2, Article number 126176. https://doi.org/10.1016/j.jmaa.2022.126176
- J. López-Gómez, J. C. Sampedro. Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier. Journal of Fixed Point Theory and Applications. 2022, 24, 1, Article number 8. https://doi.org/10.1007/s11784-021-00916-7
- J. López-Gómez, J. C. Sampedro. New analytical and geometrical aspects of the algebraic multiplicity. Journal of Mathematical Analysis and Applications. 2021, 504, 1, 125375. https://doi.org/10.1016/j.jmaa.2021.125375
- J. López-Gómez, J. C. Sampedro. Global Perturbation of Nonlinear Eigenvalues. Advanced Nonlinear Studies. 2021, https://doi.org/10.1515/ans-2021-2127
- J. López-Gómez, J. C. Sampedro. Algebraic multiplicity and topological degree for Fredholm operators. Nonlinear Analysis. 2020, 201, 112019. https://doi.org/10.1016/j.na.2020.112019