An inverse problem for an elliptic partial differential equation Academic Article uri icon

abstract

  • We demonstrate uniqueness and local existence of the unknown coefficient a = a(x) in the elliptic equation Δu - a(x) u = 0 in the quarter plane x > 0, y > 0 which is subject to the boundary conditions u(0, y) = f{hook}(y), ux(0, y) = g(y), and u(x, 0) = h(x). The proof consists of the derivation of an integral equation for a(x) utilizing transformations of Gelfand-Levitan type. © 1987.

author list (cited authors)

  • Cannon, J. R., & Rundell, W.

citation count

  • 15

publication date

  • September 1987