Sturm–Liouville boundary value problems with operator potentials and unitary equivalence

Sturm-Liouville boundary value problems with operator potentials and unitary equivalence

Consider the minimal Sturm-Liouville operator A = Amin generated by the differential expression

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Boundary Value Problems for a Class of Elliptic Operator Pencils

In this paper operator pencils A(x,D, λ) are studied which act on a manifold with boundary and satisfy the condition of N-ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich–Vishik. Sobolev spaces corresponding to the Newton polygon are defined and investigated; in particular it is possible to describe their trace spaces...

Inverse Boundary Value Problems for the Perturbed Polyharmonic Operator

We show that a first order perturbation A(x) · D + q(x) of the polyharmonic operator (−∆), m ≥ 2, can be determined uniquely from the set of the Cauchy data for the perturbed polyharmonic operator on a bounded domain in R, n ≥ 3. Notice that the corresponding result does not hold in general when m = 1.

Boundary-value Problems for the Squared Laplace Operator

The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their first (or second) normal derivatives are set to zero at the boundary. Strong ellipticity of the resulting boundary-value problems is also proved. Mixed bound...