nao André Guerra's Homepage
 
 
Home
Research
Talks
Teaching
CV
 
Home Research Talks Teaching CV

Research


Calculus of Variations and quasiconformal maps

  1. Regularity and compactness for critical points of degenerate polyconvex energies.
    With R. Tione. Submitted (2024).
  2. Lower semicontinuity, Stoilow factorization and principal maps.
    With K. Astala, D. Faraco, A. Koski, and J. Kristensen. Submitted (2024).
  3. Unique continuation for differential inclusions.
    With G. De Philippis and R. Tione. Submitted (2023).
  4. The local Burkholder functional, quasiconvexity and Geometric Function Theory.
    With K. Astala, D. Faraco, A. Koski, and J. Kristensen. Submitted (2023).
  5. Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands.
    With J. Kristensen. Archive for Rational Mechanics and Analysis, no. 2 (2022): 479–500.
  6. Numerical evidence towards a positive answer to Morrey's problem.
    With R. Teixeira da Costa. Revista Matemática Iberoamericana, 38, no. 2 (2022): 601-614.
  7. Remarks on Ornstein's non-inequality in R2x2.
    With D. Faraco. The Quarterly Journal of Mathematics, 72, no. 1 (2021): 17-21.
  8. Extremal rank-one convex integrands and a conjecture of Šverák.
    Calculus of Variations and Partial Differential Equations, 58, no. 201 (2019).

Harmonic maps and related topics

  1. Constraint maps: singularities vs free boundaries.
    With A. Figalli, S. Kim, and H. Shahgholian. In preparation (2024).
  2. Constraint maps with free boundaries: the Bernoulli case.
    With A. Figalli, S. Kim, and H. Shahgholian. Submitted (2023).
  3. Energy minimisers with prescribed Jacobian.
    With L. Koch and S. Lindberg. Archive for Rational Mechanics and Analysis, 242, no. 2 (2021): 1059-1090.
  4. The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces.
    With L. Koch and S. Lindberg. Calculus of Variations and Partial Differential Equations, 60, no. 55 (2021).

Stability in Analysis and Geometry

  1. Optimal quantitative stability of the Möbius group of the sphere in all dimensions.
    With X. Lamy and K. Zemas. Submitted (2024).
  2. Sharp quantitative stability of the Möbius group among sphere valued maps in arbitrary dimension.
    With X. Lamy and K. Zemas. Submitted (2023).
  3. Stability of the Faber-Krahn inequality for the Short-time Fourier Transform.
    With J. Goméz, J. P. Ramos, and P. Tilli. Inventiones Mathematicae, 236 (2024), 779–836.

Compensation effects in PDE

  1. Oscillations in wave map systems and homogenization of the Einstein equations in symmetry.
    With R. Teixeira da Costa, (2021). Submitted.
  2. Compensation phenomena for concentration effects via nonlinear elliptic estimates.
    With B. Raiţă and M. Schrecker. Ars Inveniendi Analytica, Paper No. 1 (2024), 56 pp.
  3. Nonlinear open mapping principles with applications to the Jacobian equation and other scale-invariant PDEs.
    With L. Koch and S. Lindberg. Advances in Mathematics, 415 (2023): 108869.
  4. Compensated Compactness: continuity in optimal weak topologies.
    With B. Raiţă and M. Schrecker. Jornal of Functional Analysis, 283, no. 7 (2022): 109596.
  5. Quasiconvexity, null Lagrangians, and Hardy integrability under constant rank constraints.
    With B. Raiţă. Archive for Rational Mechanics and Analysis, no. 2 (2022): 279–320.
  6. On the necessity of the constant rank condition for Lp estimates.
    With B. Raiţă. Comptes Rendus. Mathématique, 358, no. 9-10 (2020): 1091-1095.