Research

Research interests

  • Variational Methods
  • Nonlinear partial differential equations
  • Mathematical Analysis
  • Analysis on metric measure spaces
Vibrant sunset over the ocean with silhouettes of breakwaters and a lighthouse in the foreground.
Sunrise, Shiretoko.

Scientific Publications

(AUTHORS ORDERED ALPHABETICALLY)

Preprints

  1. “Pointwise boundary estimates for nonuniformly elliptic energy integrals with (p,q)-growth“. A. Nastasi, C. Pacchiano Camacho. (2025).
  2. “Vectorial Double Phase Obstacle Problems”. F. De Filippis, A. Nastasi, C. Pacchiano Camacho. (2025). [arXiv].
  3. “On the Lavrentiev gap for manifold-valued maps”. C.A. Antonini, F. De Filippis, C. Pacchiano Camacho. (2025). [arXiv].

Published Papers

  1. “Unified a-priori estimates for minimizers under p, q−growth and exponential growth”, P. Marcellini, A. Nastasi, C. Pacchiano Camacho. (Oct. 2025). Nonlinear Anal. [DOI]. [arXiv].
  2. “Regularity results for quasiminima of a class of double phase problems“. A. Nastasi, C. Pacchiano Camacho. (July 2024). Math. Ann. [DOI]. [arXiv].
  3. “Gradient higher integrability for double phase problems on metric measure spaces”. J. Kinnunen, A. Nastasi, C. Pacchiano Camacho. Proc. Amer. Math. Soc. Published electronically: January 18, 2024. Volume 152, Number 3, March 2024, Pages 1233–1251. [DOI]. [arXiv].
  4. “Higher integrability for quasiminimizers of a (p,q)-Dirichlet integral”, A. Nastasi, C. Pacchiano Camacho, (January 2023). Journal of Differential Equations, Volume 342, 5 January 2023, Pages 121-149. [DOI]. [arXiv].
  5. “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]. [arXiv].
  6. “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]. [arXiv].
  7. “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]. [arXiv].

In preparation

  1. “The Monge-Ampere equation and metric measure spaces”. T. Balehowsky, C. Pacchiano Camacho, C. Rios
  2. “Generalization of Ladyzhenskaya and Urall’tseva conditions to metric measure spaces”., C. Pacchiano Camacho
  3. “Local boundedness for minimizers of a class of nonlinear elliptic systems with nonstandard growth”, E. Mascolo, A. Nastasi, C. Pacchiano Camacho

Theses