I'm an Assistant Professor at Departamento de Análisis Matemático y Matemática Aplicada in Universidad Complutense de Madrid  since 2023. 

I obtained both a Bachelor’s degree in  Mathematics and Aerospace Engineering from Centre de Formació Interdisciplinària Superior (CFIS) at Universitat Politècnica de Catalunya (UPC) in 2016. During this stage, I focused my interests on Partial Differential Equations (PDE) and I started working on this topic in my Bachelor's Thesis. One year later, I obtained my Master’s degree in Advanced Mathematics and Mathematical Engineering at UPC, and I continued working on PDEs in my Master's Thesis. In May 2017, I became a PhD student at BGSMath-UPC under the supervision of Prof. Xavier Cabré supported by an FPI grant. My dissertation, titled Qualitative properties of solutions to integro-differential elliptic problems, was defended in July 2021. Between September 2021 and January 2023 I was a postdoctoral researcher at University of Helsinki (Finland).

 

Research interests

Nonlinear elliptic PDEs, Integro-differential equations, Variational problems, Minimal surfaces, Homogenization Theory.

 

Latest Publications

• X. Cabré, I. U. Erneta and J. C. Felipe-Navarro. A Weierstrass extremal field theory for the fractional Laplacian. Advances in Calculus of Variations, 17 (4). 2024. https://doi.org/10.1515/acv-2022-0099.
• A. Audrito, J.C. Felipe-Navarro and X. Ros-Oton, The Neumann problem for the fractional Laplacian: regularity up to the boundary. To appear in Annali di Scienze Scoula Normale Superiore. https://doi.org/10.2422/2036-2145.202105_096
• J.C. Felipe-Navarro, Uniqueness for linear integro-differential equations in the real line and applications. Calculus of Variations and Partial Differential Equations. 2021, 60, 220. https://doi.org/10.1007/s00526-021-02084-5
• J.C. Felipe-Navarro and T. Sanz-Perela, Semilinear integro-differential equations I: odd solutions with respect to the Simons cone. Journal of Functional Analysis. 2020, 278. https://doi.org/10.1016/j.jfa.2019.108309