1 citations · 1 across the 8 of their papers we have counts for
12 papers
Obstacles and Singularities of Riemannian Distance Functions
Paolo Albano, Piermarco Cannarsa, Carlo Sinestrari
We study the distance function from a point target in the complement of a compact obstacle endowed with a smooth Riemannian metric. We prove that the obstacle necessarily generates…
Partial Lipschitz regularity of the minimum time function for sub-Riemannian control systems
Paolo Albano, Vincenzo Basco, Piermarco Cannarsa
In Euclidean space of dimension 2 or 3, we study a minimum time problem associated with a system of real-analytic vector fields satisfying Hörmander's bracket generating condition,…
An interpolation problem in the Denjoy-Carleman classes
Paolo Albano, Marco Mughetti
Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic…
The distance function in the presence of an obstacle
Paolo Albano, Vincenzo Basco, Piermarco Cannarsa
We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First,…
On the extension problem for semiconcave functions with fractional modulus
Paolo Albano, Vincenso Basco, Piermarco Cannarsa
Consider a locally Lipschitz function on the closure of a possibly unbounded open subset of with boundary. Suppose is semiconcave on $\overline…
Generation of singularities from the initial datum for Hamilton-Jacobi equations
Paolo Albano, Piermarco Cannarsa, Carlo Sinestrari
We study the generation of singularities from the initial datum for a solution of the Cauchy problem for a class of Hamilton-Jacobi equations of evolution. For such equations, we g…
Partial regularity of minimizers for real-analytic sub-Riemannian metrics
Paolo Albano, Antonio Bove
In the real-analytic setting, we show that all sub-Riemannian minimizers (parametrized by the arc-length) are real-analytic everywhere except an at most countable non-dense set. In…
Partial regularity for solutions to subelliptic eikonal equations
Paolo Albano, Piermarco Cannarsa, Teresa Scarinci
On a bounded domain in euclidean space , we study the homogeneous Dirichlet problem for the eikonal equation associated with a system of smooth vector fields, whi…
Regularity results for the minimum time function with Hörmander vector fields
Paolo Albano, Piermarco Cannarsa, Teresa Scarinci
In a bounded domain of with smooth boundary, we study the regularity of the viscosity solution, , of the Dirichlet problem for the eikonal equation associated wit…
Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture
Paolo Albano, Antonio Bove, Marco Mughetti
We are concerned with the problem of real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this…
Singular gradient flow of the distance function and homotopy equivalence
Paolo Albano, Piermarco Cannarsa, Khai Tien Nguyen +1
It is a generally shared opinion that significant information about the topology of a bounded domain of a riemannian manifold is encoded into the properties of the distance…
Analytic Hypoellipticity in the Presence of Lower Order Terms
Paolo Albano, Antonio Bove, David S. Tartakoff
We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly to order two on a symplectic real analytic manifold. We assume that the first…