Calvin H. Wilcox

Coerciveness inequalities for nonelliptic systems of partial differential equations

AbstractThis paper deals with first-order matrix partial differential operators of the form(1)

The limiting absorption principle and spectral theory for steady-state wave propagation in inhomogeneous anisotropic media

L = - i \mathop \sum \limits_{j = 1}^n L_j (x)D_i + L_o (x)

A Coerciveness Inequality for a Class of Nonelliptic Operators of Constant Deficit.

where x=(x1, ..., xn)∈Rn, Dj=∂/∂xj, and the Lj(x), j=0, 1, 2, ..., n, are m′×m matrix-valued functions of x. Let L2, m, be the Hilbert space of square integrable m-vector-valued functions on Rn. The operator(1) determines a closed linear operator L : L2, m→L2, m′. L is said to be coercive on a subspace V⊂L2, m if there is a constant μ>0 such that(2)

A rellich uniqueness theorem for steady-state wave propagation in inhomogeneous anisotropic media

\mathop \sum \limits_{j = 1}^n \left\| {D_j u} \right\|^2 \leqslant \mu ^2 (\left\| {Lu} \right\|^2 + \left\| u \right\|^2 )

The Singularities of the Green's Matrix in Anisotropic Wave Motion.

for all u∈D(L)∩V, where D(L) denotes the domain of L and ∥·∥ denotes the norm in L2, m. L is said to have constant deficit k in Rn if the symbol