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Preprints

  1. (with H. Chang and J. C. Fernández) ''Fractional Q-curvature on the sphere and optimal partitions'', (arXiv)
  2. (with M. Clapp and J. Faya ) ''Critical equations with a sharp change of sign in the nonlinearity'', (arXiv)
  3. (with D. Schiera and H. Tavares ) ''On least energy solutions to a pure Neumann Lane-Emden system: convergence, symmetry breaking, and multiplicity'', (arXiv)
  4. (with M. Clapp and A. Pistoia ) ''Multiple solutions to a semilinear elliptic equation with a sharp change of sign in the nonlinearity'', (arXiv)
  5. (with V. Hernández-Santamaría, S. Jarohs, and L. Sinch) ''FEM for 1D-problems involving the logarithmic Laplacian: error estimates and numerical implementation'', (arXiv)

Publications

  1. (with N. Abatangelo and H. Tavares ) ''An asymptotic relationship between Lane-Emden systems and the 1-bilaplacian equation'', Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, (arXiv)
  2. (with M. Clapp and A. Szulkin ) ''On a Schrödinger system with shrinking regions of attraction'', to appear in Zeitschrift fur Angewandte Mathematik und Physik. (journal), (arXiv)
  3. (with M. Clapp, Mayra Soares, and Víctor A. Vicente-Benítez) ''Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schrödinger system'', Annali di Matematica Pura ed Applicata (2025), (journal), (arXiv)
  4. (with M. Clapp and V. Hernández-Santamaría ) ''A strong unique continuation property for weakly coupled elliptic systems'', Journal of Mathematical Analysis and Applications (2025), (journal), (arXiv)
  5. (with M. Clapp and V. Hernández-Santamaría ) ''Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction'', Nonlinear Analysis (2025), (journal), (arXiv), (Addendum)
  6. (with V. Hernández-Santamaría and L.F. López Ríos) ''Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian'', Discrete and Continuous Dynamical Systems (2025). (journal) (arXiv)
  7. (with A. Dieb and I. Ianni ) ''Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems'', Calculus of Variations and Partial Differential Equations (2024), (journal) (arXiv)
  8. (with M. Clapp and J. Faya ) ''Optimal pinwheel partitions for the Yamabe equation'', Nonlinearity (2024), (journal) (arXiv)
  9. (with S. Jarohs and T. Weth ) ''Differentiability of the nonlocal-to-local transition in fractional Poisson problems'', Potential Analysis (2024), (journal) (arXiv)
  10. (with M. Clapp and A. Szulkin ) ''Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system'', Boletín de la Sociedad Matemática Mexicana (2024). (journal) (arXiv)
  11. (with H. Chang ) ''Classical solutions to integral equations with zero order kernels'', Mathematische Annalen (2024), (journal) (arXiv)
  12. (with A. Pistoia and H. Tavares ) ''Existence of solutions to a slightly supercritical pure Neumann problem'', SIAM Journal on Mathematical Analysis (2023), (journal) (arXiv)
  13. (with A. Dieb and I. Ianni ) ''Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods'', Nonlinear Analysis (2023), (journal) (arXiv)
  14. (with F. Angeles and M. Clapp ) ''Exponential decay of the solutions to nonlinear Schrödinger systems'', Calculus of Variations and Partial Differential Equations, 62, 160 (2023), (journal) (arXiv)
  15. (with F. Angeles ) ''Small order limit of fractional Dirichlet sublinear-type problems'', Fractional Calculus and Applied Analysis (2023), (journal) (arXiv)
  16. (with H. Tavares ) ''On the least-energy solutions of the pure Neumann Lane-Emden equation'', Nonlinear Differential Equations and Applications NoDEA volume 29, Article number: 30 (2022), (journal) (arXiv)
  17. (with V. Hernández-Santamaría ) ''Small order asymptotics for nonlinear fractional problems'', Calculus of Variations and Partial Differential Equations volume 61, Article number: 92 (2022), (journal) (arXiv)
  18. (with T. Weth and J. Földes) ''Symmetry properties of sign-changing solutions to nonlinear parabolic equations in unbounded domains'', Journal of Dynamics and Differential Equations (2021), (journal) (arXiv)
  19. (with I. Ianni ) ''Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems'', Journal of Differential Equations, Volume 304, 102-164 (2021), (journal) (arXiv)
  20. (with M. Clapp and J. C. Fernández) ''Critical polyharmonic systems and optimal partitions'', Communications on Pure & Applied Analysis (2021), (journal) (arXiv)
  21. (with V. Hernández-Santamaría ) ''Existence and convergence of solutions to fractional pure critical exponent problems'', Advanced Nonlinear Studies 21 no. 4, 827-854 (2021), (journal) (arXiv)
  22. (with M. Clapp, R. Pardo, and A. Pistoia ) ''A solution to a slightly subcritical elliptic problem with non-power nonlinearity'', Journal of Differential Equations, Volume 275 (2021), (journal) (arXiv)
  23. (with N. Abatangelo and S. Jarohs ) ''Fractional Laplacians on ellipsoids'', Mathematics in Engineering, Volume 3, Issue 5: 1-34 (2021). (journal) (arXiv)
  24. ''On fractional higher-order Dirichlet boundary value problems: between the Laplacian and the bilaplacian'', Contemporary Mathematics (American Mathematical Society), Volume 775 (2021) (journal) (arXiv)
  25. (with S. Jarohs and T. Weth ) ''A new look at the fractional Poisson problem via the Logarithmic Laplacian'', Journal of Functional Analysis, Volume 279, Issue 11 (2020), (journal) (arXiv) (Addendum)
  26. (with M. Clapp and A. Szulkin ) ''Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere'', International Mathematics Research Notices (2020), (journal) (arXiv)
  27. (with M. Clapp ) ''Entire nodal solutions to the critical Lane-Emden system'', Communications in Partial Differential Equations, Volume 45, Issue 4 (2020) (journal) (arXiv)
  28. (with M. Grossi and H. Tavares ) ''Sharp concentration estimates near criticality for radial sign-changing solutions of Dirichlet and Neumann problems'', Proceedings of the London Mathematical Society Volume 120, Issue 1 (2020) (journal) (arXiv)
  29. (with N. Abatangelo , S. Dipierro, M.M. Fall , and S. Jarohs ) ''Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions'', Discrete Contin. Dyn. Syst. 39(3): 1205-1235 (2019) (journal) (arXiv)
  30. (with N. Abatangelo and S. Jarohs ) ''Positive powers of the Laplacian: from hypersingular integrals to boundary value problems'', Communications on Pure & Applied Analysis, 17 (3) : 899-922. (2018) (journal) (arXiv)
  31. (with N. Abatangelo and S. Jarohs ) ''Integral representation of solutions to higher-order fractional Dirichlet problems on balls'', Communications in Contemporary Mathematics, Vol. 20, No. 08, (2018) (journal) (arXiv) (Addendum)
  32. (with H. Tavares ) ''Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions'', Journal of Differential Equations, Volume 265, Issue 12, 15, pages 6127-6165 (2018) (journal) (arXiv)
  33. (with N. Abatangelo and S. Jarohs ) ''On the loss of maximum principles for higher-order fractional Laplacians'', Proceedings of the American Mathematical Society, Volume 146, Number 11, pages 4823–4835 (2018) (journal) (extended preprint)
  34. (with N. Abatangelo and S. Jarohs ) ''Green function and Martin kernel for higher-order fractional Laplacians in balls'', Nonlinear Analysis, Volume 175, pages 173-190 (2018) (journal) (PDF) (extended preprint) (Addendum)
  35. (with D.Bonheure , J. Földes , E. Moreira dos Santos , and H. Tavares ) ''Paths to Uniqueness of Critical Points and Application to Partial Differential Equations'', Transactions of the American Mathematical Society, 370, 7081-7127 (2018) (journal) (arXiv)
  36. Partial symmetry of solutions to parabolic problems via reflection methods, Rend. Sem. Mat. Univ. Pol. Torino (2017) (journal)
  37. (with D.Bonheure and J. Földes ) ''Qualitative properties of solutions to mixed-diffusion bistable equations'', Calc. Var. Partial Differential Equations 55, no. 3, Paper No. 67, 23 pp (2016) (journal) (arXiv)
  38. ''Qualitative properties of coexistence and semi-trivial limit profiles of nonautonomous nonlinear parabolic Dirichlet systems'', Nonlinear Analysis: Theory, Methods & Applications, Volume 130, 31–46 (2016) (journal) (arXiv)
  39. (with T. Weth ) ''On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems'', Journal of Dynamics and Differential Equations 27, no. 2, 307–332 (2015) (journal) (arXiv)
  40. (with T. Weth ) ''Asymptotic axial symmetry of solutions of parabolic equations in bounded radial domains'', Journal of Evolution Equations, Volume 12, Issue 3, 697-712 (2012) (journal) (arXiv).

Ph.D. Thesis

  1. ''Partial symmetries of solutions to nonlinear elliptic and parabolic problems in bounded radial domains'', PhD thesis, Johann Wolfgang Goethe-Universität Frankfurt am Main, Germany, 2014. (PDF)