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 partial differential equation problems from various areas of mathematical physics; all are analysed in a unified manner, known results are recovered and new ones established.
Krejčiřík, D., Raymond, N., Royer, J., & Siegl, P. (2018). REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM-RESOLVENT CONVERGENCE AND APPLICATIONS. Mathematika, 64(2), 406–429. https://doi.org/10.1112/S0025579318000013