Titlebook: Harnack Inequalities and Nonlinear Operators; Proceedings of the I Vincenzo Vespri,Ugo Gianazza,Daniele Andreucci Conference proceedings 20

Functional

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,A Short Presentation of Emmanuele’s Work,As the title suggests, this is a short presentation of DiBenedetto’s mathematical work. In the first part Ugo Gianazza gives a general overview, without entering too much into details of specific papers; in his contribution Daniele Andreucci focuses on DiBenedetto’s accomplishments in BioMathematics.

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,Monotonicity of Positive Solutions to ? Δ,,?+?,(,)|?,|,?=?,(,) in the Half-Plane in the Case ,,We consider a quasilinear elliptic equation involving a first order term, under zero Dirichlet boundary condition in the half-plane. We prove that any positive possibly unbounded solution, is monotone increasing with respect to the direction orthogonal to the boundary.

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