## Research interests

- Mathematical Analysis
- Nonlinear partial differential equations
- Analysis on metric measure spaces
- Variational Methods

## Scientific Publications

### Published Papers

**“**A. Nastasi, C. Pacchiano Camacho, (January 2023). Journal of Differential Equations, Volume 342, 5 January 2023, Pages 121-149. [DOI].**Higher integrability for quasiminimizers of a (p,q)-Dirichlet integral”,****“Variational solutions to the total variation flow on metric measure spaces”,**V. Buffa, J. Kinnunen, C. Pacchiano Camacho. (July 2022), Nonlinear Analysis; Volume 220, 112859; [DOI].**“Existence of parabolic minimizers to the total variation flow on metric measure spaces”,**V. Buffa, M. Collins, C. Pacchiano Camacho, (January 2022). manuscripta mathematica; [DOI].**“Regularity properties for quasiminimizers of a (p,q)-Dirichlet integral”**, A. Nastasi, C. Pacchiano Camacho. (December 2021). Calculus of Variations and Partial Differential Equations; 60 (6); [DOI].

### Preprints

- See
**“In preparation”**section below.

### In preparation

**“Higher integrability of double phase variational integrals on metric measure spaces”.**J. Kinnunen, A. Nastasi, C. Pacchiano Camacho.**“Regularity Properties for the Double Phase on Metric Measure Spaces“.**A. Nastasi, C. Pacchiano Camacho**“The Monge-Ampere equation and metric measure spaces“.**T. Balehowsky, C. Pacchiano Camacho, C. Rios**“Limit as p tends to infinity of the p-Laplacian on metric measure spaces“.**C. Pacchiano Camacho

### Theses

**Ph.D. Thesis:**“Nonlinear variational problems on metric measure spaces”.*Supervising professor:*Prof. Juha Kinnunen, Aalto University, Finland.*Thesis advisor:*Prof. Juha Kinnunen, Aalto University, Finland.*Preliminary examiners:*Prof. Anna Zatorska-Goldstein, University of Warsaw, Poland.

Prof. Simone Di Marino, Università di Genova, Italy.*Opponent:*Prof. Cristiana De Filippis, University of Parma, Italy.*Date of public defence:*23rd of September 2022. [Press release] [slides]**Master’s Thesis:**“Hilbert expansions in kinetic equations”*Advisor:*Prof. Dr. Juan J.L. Velázquez,*Second Advisor:*Dr. Alessia Nota

Mathematical Institute, University of Bonn. [Summary]**Bachelor’s Thesis:**“El problema de Brezis-Nirenberg”*Advisor:*Prof. Dr. Mónica Alicia Clapp Jiménez-Labora

Facultad de Ciencias, UNAM. México. [Summary]