Research

Published or Accepted Papers

[12] D.Di Donato, Le Donne, “Intrinsically Lipschitz sections and applications to metric group”, accepted to Communications in Contemporary Mathematics, 2024

[11] V.Ambrosio, D.Di Donato, “An existence result for a fractional critical (p,q)-Laplacian problem with discontinuous nonlinearity”, Mediterranean Journal of Mathematics, 20, 288 (2023), https://doi.org/10.1007/s00009-023-02478-z

[10] D.Di Donato, “The intrinsic Hopf-Lax semigroup vs. the intrinsic slope”, accepted to Journal of Mathematical Analysis and Applications, Volume 523, Issue 2, 15 July 2023, 127051,  https://doi.org/10.1016/j.jmaa.2023.127051.

[9] D.Di Donato, “Some remarks about intrinsic Lipschitz and tame maps in Carnot groups of step 2”, Riv. Mat. Univ. Parma, Volume 14, Number 1, 2023, http://www.rivmat.unipr.it/vols/2023-14-1/index-vol14-1.html

[8] G.Antonelli, D.Di Donato, S.Don, “Distributional solutions of Burgers’ type equations for intrinsic graphs in Carnot group of step 2”, Potential Analysis, Volume 59, pages 1481–1506, (2023), https://doi.org/10.1007/s11118-022-09992-x

[7] G.Antonelli, D.Di Donato, S.Don, E.Le Donne, “Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups”, accepted to Annales de l’Institut Fourier, 2022, arXiv:2005.11390

[6] D.Di Donato, K.Fässler, “Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups”, Annali di Matematica Pura e Applicata 201, 453–486 (2022) https://link.springer.com/article/10.1007/s10231-021-01124-3

[5] D.Di Donato, K.Fässler, T.Orponen, “Metric rectifiability of H-regular surfaces with Hölder continuous horizontal normal”, International Mathematics Research Notices, Volume 2022, Issue 22, November 2022, Pages 17909-17975 (2021), https://doi.org/10.1093/imrn/rnab227,  arXiv:1906.10215

[4] D.Di Donato – “Intrinsic Lipschitz graphs in Carnot groups of step 2”, Annales Academiæ Scientiarum Fennicæ Mathematica,  Volumen 45, (2020), 1013–1063, https://doi.org/10.5186/aasfm.2020.4556

[3] D.Di Donato – “Intrinsic differentiability and Intrinsic Regular Surfaces in Carnot groups”, Potential Analysis,  Volumen 54, 1-39, 2021, https://link.springer.com/article/10.1007/s11118-019-09817-4

[2] D.Di Donato – “Intrinsic differentiability and Intrinsic Regular Surfaces in Carnot groups”, PhD thesis at University of Trento, 2017

[1] D.Di Donato, D.Mugnai – “On a Highly Nonlinear Self-Obstacle Optimal Control Problem”, Applied Mathematics & Optimization: Vol. 72, Issue 2 (2015), Page 261-290. https://link.springer.com/article/10.1007/s00245-014-9279-8

Preprints

[a] D.Di Donato, “Normed spaces using intrinsically Lipschitz sections and Extension Theorem for the intrinsically Hölder sections”, preprint, arxiv.2301.01735

[b] D.Di Donato, “Non-symmetric intrinsic Hopf-Lax semigroup vs. intrinsic Lagrangian”, preprint, arxiv.2211.12822

[c] D.Di Donato, “Intrinsic Cheeger energy for the intrinsically Lipschitz constants, preprint, arxiv.2205.15851

[d] D.Di Donato, “Intrinsically quasi-isometric sections in metric spaces”, preprint, arxiv.2205.03351

[e] D.Di Donato, “Intrinsically Hölder sections in metric spaces”, preprint, arxiv.2205.02688

[f] D.Di Donato, “A note about intrinsically Lipschitz constants”, preprint, arxiv.2205.02404

[g] D.Di Donato, “Intrinsically Lipschitz graphs on semidirect products of groups”, preprint, arxiv.2205.02403

[i] D.Di Donato, “Ahlfors-David regularity of intrinsically quasi-symmetric sections in metric spaces”, preprint, arxiv.2205.02400

[l] D.Di Donato, “Intrinsic Lipschitz maps vs. Lagrangian type solutions in Carnot groups of step 2”, preprint, arXiv:2108.02298