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A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition

Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, via Cintia–Complesso Universitario Monte S. Angelo, 80126 Naples, Italy

E-mail Address: annamaria.barbagallo@unina.it

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and

Vincenzo Esposito

Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, via Cintia–Complesso Universitario Monte S. Angelo, 80126 Naples, Italy

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https://doi.org/10.1142/S0219891619500097Cited by:2 (Source: Crossref)

Abstract

We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent $s \leq 0$ for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space $ℝ^{3}$ .

Communicated by T. Nishitani

Keywords:

AMSC: 35B45, 47G30, 35S05, 35L10

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