arXiv subjects
Publications and source records attributed to Claudio Marchi.
We generalize the results in [16] to higher dimensional ramified spaces. For this purpose we introduce ramified manifolds and, as special cases, locally elementary polygonal ramified spaces (LEP spaces). On LEP spaces we develop a theory of viscosity solutions for Hamilton-Jacobi equations, providing existence and uniqueness results.
This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators (briefly, HJBI). For the parabolic Cauchy problem, we establish such an estimate in the whole space $[0,+\infty)\times\Rn$. Moreover, under some periodicity and ellipticity assumptions, we obtain a similar estimate for the ergodic constant associated to the HJBI operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.