Piermarco Cannarsa

Second-order Hamilton-Jacobi equations in infinite dimensions

Some second-order Hamilton–Jacobi equations connected to stochastic optimal control problems for infinite-dimensional systems driven by a white noise are studied. A direct method to prove existence and uniqueness of mild solutions is developed. Then this solution is identified as the value function of the related stochastic control problem, and a feedback formula for optimal controls is derived.

Determination of source terms in a degenerate parabolic equation

In this paper, we prove Lipschitz stability results for inverse source problems relative to parabolic equations. We use the method introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates. What is new here is that we study a class of one-dimensional degenerate parabolic equations. In our model, the diffusion coefficient vanishes at one extreme point of the domain. Instead of the classical Carleman estimates obtained by Fursikov and Imanuvilov for non degenerate equations, we use and extend some recent Carleman estimates for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble. Finally, we obtain Lipschitz stability results in inverse source problems for our class of degenerate parabolic equations both in the case of a boundary observation and in the case of a locally distributed observation.

Null controllability of Grushin-type operators in dimension two

We study the null controllability of the parabolic equation associated with the Grushintype operator

On the Bellman Equation for the Minimum Time Problem in Infinite Dimensions

A = \partial_x^2 + |x|^{2\gamma}\partial_y^2 (\gamma > 0)

Nonlinear optimal control with infinite horizon for distributed parameter systems and stationary Hamilton-Jacobi equations

in the rectangle

Generation of analytic semigroups in theL p topology by elliptic operators inR n

\Omega = (-1, 1) \times (0, 1)

Unique continuation and approximate controllability for a degenerate parabolic equation

, under an additive control supported in an open subset

Singular gradient flow of the distance function and homotopy equivalence

\omega

On a Differential Model for Growing Sandpiles with Non-Regular Sources

of

Hölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equations

\Omega