Gap in the essential spectrum of an elliptic formally self-adjoint system of differential equations
С. А. Назаров · Differential Equations · 2010
For a formally self-adjoint elliptic system of partial differential equations with periodic coefficients in the space ℝ n , we show that, by conferring contrast properties to the coefficients of differential operators, one can open a gap in the essential spectrum of the system. We suggest a method based on the derivation of an asymptotically sharp generalized Korn inequality and the use of the maximin principle; this method applies to perforated media as well as to periodic layered and quasi-cylindrical waveguides.