Solving problem on faithful transfer of Sommerfeld radiation condition to a boundary of a bounded in 3D space

Abstract

In this paper it’s proved Reley-Faber-Kranh inequality for Laplace operator with boundary condition of the Newton potential. The terms of the flat areas is minimizing (among other regions of the same area) the first eigenvalue Laplacian with Dirichlet boundary condition. Musical interpretation is among all the drums with a given Square, circular drum to produce the lowest purity. Historically, the minimization of the first eigenvalue of the Laplacian, probably one of the first of such problems, which appeared in the scientific literature. In fact, in his famous book Rayleigh "Theory sounds "[1] (the first was published in 1877), which focuses on some explicit computation and physical interpretation, it is argued that the terms of the flat area is minimized (among regions of equal area) of the first eigenvalue Laplacian with Dirichlet boundary condition. Musical Interpretation This result sledyuschee: among all the drums with a given Square, circular drum to produce the lowest frequency.