Reduction of dimension as a consequence of norm-resolvent convergence and applications

David Krejcirik (1) , Nicolas Raymond (2) , Julien Royer (3) , Petr Siegl (4)

1 CTU - Czech Technical University in Prague
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]

This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its application on seemingly different PDE problems from various areas of mathematical physics; all are analysed in a unified manner now, known results are recovered and new ones established.

Domaines: Mathématiques [math]

David Krejcirik, Nicolas Raymond, Julien Royer, Petr Siegl. Reduction of dimension as a consequence of norm-resolvent convergence and applications. Mathematika, 2018, 64 (2), pp.406-429. ⟨10.1112/S0025579318000013⟩. ⟨hal-01449405⟩