Abstract We consider the problem of determining, within an elastic isotropic nanoplate in bending, possible presence inclusion made different material. Under suitable a priori assumptions on unknown inclusion, we provide quantitative upper and lower estimates for area defect terms works exerted by boundary data when is present it absent.

Abstract We obtain the optimal version of Cwikel-type estimates for uniform operator norm which implies optimality M.Z. Solomyak’s results (Proc. Lond. Math. Soc. 71(1):53–75, 1995) within classes Orlicz/Lorentz spaces. Our methods are based on finding distributional Sobolev inequality.