Giulio Galise
Curriculum Vitae
ITA
ENG
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
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I. Birindelli, G. Galise, H. Ishii Propagation of minima for nonlocal operators, to appear on Proc. A Royal Soc. Edinburgh
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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)
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I. Birindelli, G. Galise, E. Topp, Fractional truncated Laplacians: representation formula, fundamental solutions and applications, Nonlinear Differ. Equ. Appl. 29, 26, 1-49 (2022)
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F. Ferrari, G. Galise, A regularity result for a class of non-uniformly elliptic operators, Arch. Math. 118, 539–548 (2022)
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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)
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I. Birindelli, G. Galise, H. Ishii, Existence through convexity for the truncated Laplacians, Mathematische Annalen, volume 379, pages 909-950 (2021)
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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)
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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)
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I. Birindelli, G. Galise Allen-Cahn equation for the truncated Laplacian: unusual phenomena, Mathematics in Engineering, 2(4): 722–733 (2020)
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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)
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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)
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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)
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G. Galise, On positive solutions of fully nonlinear degenerate Lane-Emden type equations, J. Differential Equations, 266, 1675-1697 (2019)
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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)
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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)
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I. Birindelli, G. Galise, F. Leoni, Liouville theorems for a family of very degenerate elliptic nonlinear operators, Nonlinear Analysis, 161, 198-211 (2017)
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G. Galise, F. Leoni, F. Pacella, Existence results for fully nonlinear equations in radial domains, Commun. Partial Differential Equations, 42:5, 757-779 (2017)
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G. Galise, A. Vitolo, Removable singularities for degenerate elliptic Pucci operators, Adv. Differential Equations 22 no. 1/2, 77-100 (2017)
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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)
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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)
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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)
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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)
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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