Giulio Galise

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Research

Teaching

Curriculum Vitae

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Main fields
Nonlinear partial differential equations

Keywords: Fully nonlinear elliptic (local and non local) equations, viscosity solutions, degenerate ellipticity, maximum principles, principal eigenvalues, critical exponents, concentration phenomena, Hamilton-Jacobi equations, homogenization.

Publications

  1. I. Birindelli, G. Galise, H. Ishii Propagation of minima for nonlocal operators, Proc. A Royal Soc. Edinburgh 154, 1033–1046 (2024)

  2. I. Birindelli, G. Galise, D. Schiera, Maximum principles and related problems for a class of nonlocal extremal operators, Ann. Mat. Pura Appl. 201: 2371-2412 (2022)

  3. I. Birindelli, G. Galise, E. Topp, Fractional truncated Laplacians: representation formula, fundamental solutions and applications, Nonlinear Differ. Equ. Appl. 29, 26, 1-49 (2022)

  4. F. Ferrari, G. Galise, A regularity result for a class of non-uniformly elliptic operators, Arch. Math. 118, 539–548 (2022)

  5. I. Birindelli, G. Galise, A. Rodriguez Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians, Journal of Convex Analysis, 28, No. 2, 329-352 (2021)

  6. I. Birindelli, G. Galise, H. Ishii, Existence through convexity for the truncated Laplacians, Mathematische Annalen, volume 379, pages 909-950 (2021)

  7. I. Birindelli, G. Galise, H. Ishii, Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle , Trans. Amer. Math. Soc., 374 (1), 539-564 (2021)

  8. G. Galise, A. Iacopetti, F. Leoni, F. Pacella New concentration phenomena for a class of radial fully nonlinear equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 37, 1109-1141 (2020)

  9. I. Birindelli, G. Galise Allen-Cahn equation for the truncated Laplacian: unusual phenomena, Mathematics in Engineering, 2(4): 722–733 (2020)

  10. G. Galise, A. Iacopetti, F. Leoni, Liouville-type results in exterior domains for radial solutions of fully nonlinear equations, J. Differential Equations, 269, 5034-5061 (2020)

  11. I. Birindelli, G. Galise, H. Ishii, Towards a reversed Faber-Krahn inequality for the truncated Laplacian, Rev. Mat. Iberoam., Volume 36, Issue 3, pp. 723–740, (2020)

  12. I. Birindelli, G. Galise, The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity, Calc. Var. Partial Differential Equations 58, no. 5, Art. 180 (2019)

  13. G. Galise, On positive solutions of fully nonlinear degenerate Lane-Emden type equations, J. Differential Equations, 266, 1675-1697 (2019)

  14. I. Birindelli, G. Galise, F. Leoni, F. Pacella, Concentration and energy invariance for a class of fully nonlinear elliptic equations, Calc. Var. Partial Differential Equations 57, no. 6, Art. 158, 22 pp (2018)

  15. I. Birindelli, G. Galise, H. Ishii, A family of degenerate elliptic operators: Maximum principle and its consequences, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 35, 417-441 (2018)

  16. I. Birindelli, G. Galise, F. Leoni, Liouville theorems for a family of very degenerate elliptic nonlinear operators, Nonlinear Analysis, 161, 198-211 (2017)

  17. G. Galise, F. Leoni, F. Pacella, Existence results for fully nonlinear equations in radial domains, Commun. Partial Differential Equations, 42:5, 757-779 (2017)

  18. G. Galise, A. Vitolo, Removable singularities for degenerate elliptic Pucci operators, Adv. Differential Equations 22 no. 1/2, 77-100 (2017)

  19. G. Galise, S. Koike, O. Ley, A. Vitolo, Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term, J. Math. Anal. Appl. 441, 194-210 (2016)

  20. G. Galise, C. Imbert, R. Monneau, A junction condition by specified homogenization and application to traffic lights, Analysis & PDE, Vol. 8, No. 8, 1891-1929 (2015)

  21. M.E. Amendola, G. Galise, A. Vitolo, On the uniqueness of blow-up solutions of fully nonlinear elliptic equations, Discrete and Continuous Dynamical Systems - Series S, Vol. 2013, Issue special, 771-780 (2013)

  22. M.E. Amendola, G. Galise, A. Vitolo, Riesz capacity, maximum principle and removable sets of fully nonlinear second order elliptic operators, Differential and Integral equations, Vol. 26, 845-866 (2013)

  23. G. Galise, A. Vitolo, Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity, Int. J. Differ. Equ., vol. 2011, 1-18 (2011)

Preprints

  • I. Birindelli, L. Du, G. Galise, Liouville results for semilinear integral equations with conical diffusion , arXiv:2406.12720

  • I. Birindelli, G. Galise, Y. Sire, Nonlocal degenerate Isaacs operators: H\"older regularity , arXiv: 2310.11111