Top-level heading

On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians

Categoria
Seminari di Analisi Matematica
Data e ora inizio evento
Data e ora fine evento
Aula
Sala di Consiglio
Sede

Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Speaker

Andrea Davini (Sapienza Università di Roma)

We consider the discounted approximation of the critical Hamilton-Jacobi equation set on the real line associated with the Hamiltonian G(x,p):=H(x,p)-V(x), where H is a 1-periodic Tonelli Hamiltonian and V is a continuous and compactly supported potential. The critical constant associated with G is characterized as the unique constant a for which the associated HJ equation G(x,u')=a can have globally bounded solutions. We prove that the solutions of the discounted equation converge to a specific critical solution, which is identified in terms of projected Mather measures for G and of the asymptotic solution of the unperturbed periodic problem. This is joint work with I. Capuzzo-Dolcetta.