8 papers
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,…
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…