Limiting absorption principle for the dissipative Helmholtz equation

Julien Royer (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the resolvent estimates for the high frequency Helmholtz equation when trapped trajectories meet the set where the imaginary part of the potential is non-zero. We also give the resolvent estimates in Besov spaces.

Mots clés: Selfadjoint dilations; Dissipative operators; Helmholtz equation; limiting absorption principle; Mourre's commutator method; Selfadjoint dilations.

Domaines: Equations aux dérivées partielles [math.AP]

Julien Royer. Limiting absorption principle for the dissipative Helmholtz equation. Communications in Partial Differential Equations, 2010, 25 (8), p. 1458-1489. ⟨10.1080/03605302.2010.490287⟩. ⟨hal-00380641v2⟩