40 citations · 50 across the 14 of their papers we have counts for
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Heat equation on the Heisenberg group: observability and applications
Karine Beauchard, Piermarco Cannarsa
We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain taking as observation…
Singularities of solutions of Hamilton-Jacobi equations
Piermarco Cannarsa, Wei Cheng
This is a survey paper on the quantitative analysis of the propagation of singularities for the viscosity solutions to Hamilton-Jacobi equations in the past decades. We also review…
Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
Piermarco Cannarsa, Wei Cheng, Albert Fathi
If is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation where is a not necessaril…
Herglotz' variational principle and Lax-Oleinik evolution
Piermarco Cannarsa, Wei Cheng, Liang Jin +2
We develop an elementary method to give a Lipschitz estimate for the minimizers in the problem of Herglotz' variational principle proposed in \cite{CCWY2018} in the time-dependent…
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…
Inverse coefficient problems for a transport equation by local Carleman estimate
Piermarco Cannarsa, Giuseppe Floridia, Fikret Gölgeleyen +1
We consider the transport equation $\ppp_tu(x,t) + (H(x)\cdot \nabla u(x,t)) + p(x)u(x,t) = 0$ in $\OOO \times (0,T)$ where $\OOO \subset \R^n$ is a bounded domain, and discuss two…