Spectral asymptotics of variational problems with pseudodifferential constraints (Q1907471)

The spectral asymptotics of the quotient of two differential quadratic forms whose arguments are vector functions on a bounded domain \(\Omega\subset \mathbb{R}^n\), \(\partial \Omega\in C^\infty\) are studied. These two forms are defined on a subspace of an appropriate Sobolev space \(H^k(\Omega)\). The author gives a formula for the leading term of the asymptotics of the spectrum. This paper can be viewed as a continuation of some previous investigations of Birman and Solomyak. An interesting spectral problem arising in hydrodynamics is discussed at the end of the paper.