Papers by Annamaria Montanari
The scope of this conference has been to celebrate the 65th birthday of Ermanno Lanconelli and to... more The scope of this conference has been to celebrate the 65th birthday of Ermanno Lanconelli and to bring together italian and foreign Mathematicians to promote the discussion in the areas of research where Ermanno Lanconelli has been particularly active:- Second order linear and nonlinear partial differential equations with non-negative characteristic form- Geometric problems related to the underlying algebraic, geometrical or topological structure- Application to complex geometry and CR manifoldsThese fields are the objects of active research and development, and possess a remarkable degree of interrelation in their pure and applied aspects. In particular they find natural applications in mathematical finance, in the description of the visual cortex and in image processing
Calculus of Variations and Partial Differential Equations
For cost functions c(x, y) = h(x − y) with h ∈ C 2 homogeneous of degree p ≥ 2, we show L ∞-estim... more For cost functions c(x, y) = h(x − y) with h ∈ C 2 homogeneous of degree p ≥ 2, we show L ∞-estimates of Tx − x on balls, where T is an h-monotone map. Estimates for the interpolating mappings T t = t(T − I) + I are deduced from this.
Equazioni a derivate parziali.-Smooth regularity for solutions of the Levi Monge-Ampère equation.... more Equazioni a derivate parziali.-Smooth regularity for solutions of the Levi Monge-Ampère equation. Nota di Francesca Lascialfari e Annamaria Montanari, presentata (*) dal Socio F. Ricci.
Nonlinear Analysis, 2018
We develop an abstract theory to obtain Harnack inequality for non homogeneous PDEs in the settin... more We develop an abstract theory to obtain Harnack inequality for non homogeneous PDEs in the setting of quasi metric spaces. The main idea is to adapt the notion of double ball and critical density property given by Di Fazio, Gutiérrez, Lanconelli, taking into account the right hand side of the equation. Then we apply the abstract procedure to the case of subelliptic equations in non divergence form involving Grushin vector fields and to the case of X-elliptic operators in divergence form.
Annali di Matematica Pura ed Applicata (1923 -), 2020
Contents 1 Introduction 1 2 Preliminaries 4 3 Multiexponentials in filiform groups. 7 4 Inner con... more Contents 1 Introduction 1 2 Preliminaries 4 3 Multiexponentials in filiform groups. 7 4 Inner cone property for horizontally convex sets 10 4.
Communications in Partial Differential Equations, 2001
We prove, with a real analysis technique, the smooth regularity of classical solutions to a nonli... more We prove, with a real analysis technique, the smooth regularity of classical solutions to a nonlinear degenerate parabolic PDE with initial data C . This equation arises in the study of the geometric properties of the motion by the trace of the Levi form of a real hypersurface in C with Levi curvature different from zero at every point and which is locally the graph of a C function.
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 2003
In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex fu... more In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous H-convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for the class of continuous H-convex functions in the Heisenberg group.
We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two wi... more We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators. We also calculate explicitly the cut time of any extremal path and the distance from the origin of all points of the cut locus. Finally, by using the Hamiltonian approach, we show that the cut time of strictly normal extremal paths is a smooth explicit function of the initial velocity covector. Finally, using our previous results, we show that at any cut point the distance has a corner-like singularity.
We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere ty... more We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere type operator on the Heisenberg group. A notion of normal mapping does not seem to be available in this context and the method of proof uses integration by parts and oscillation estimates that lead to the construction of an analogue of Monge-Ampere measures for convex functions in the Heisenberg group.
Contemporary Mathematics, 2013
Lecture Notes in Mathematics, 2014
Calculus of Variations and Partial Differential Equations
We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two wi... more We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators, giving a new, independent proof of a result by Myasnichenko [Mya02]. We also calculate explicitly the cut time of any extremal path and the distance from the origin of all points of the cut locus. Furthermore, by using the Hamiltonian approach, we show that the cut time of strictly normal extremal paths is a smooth explicit function of the initial velocity covector. Finally, using our previous results, we show that at any cut point the distance has a corner-like singularity.
We prove integral formulas for closed hypersurfaces in C n+1 , which furnish a relation between e... more We prove integral formulas for closed hypersurfaces in C n+1 , which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then we follow the Reilly approach to prove an isoperimetric inequality. As an application, we obtain the "Soap Bubble Theorem" for starshaped domains with positive and constant Levi curvatures bounding the classical mean curvature from above.
Communications on Applied Nonlinear Analysis, 2003
Annales De L Institut Fourier, 2004
Springer INdAM Series, 2015
tu se' lo mio maestro e 'l mio autore tu se' solo colui da cu' io tolsi lo bello stilo che m'ha f... more tu se' lo mio maestro e 'l mio autore tu se' solo colui da cu' io tolsi lo bello stilo che m'ha fatto onore.
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Papers by Annamaria Montanari