Crack jump conditions for elliptic problems

We derive jump conditions for a potential function and its derivatives acro ss a crack. A crack is a "thin" region of very different conductivity, for example a fracture in otherwise homogeneous material. Such a sharp change o f material properties introduces a discontinuity in the coefficient of the elliptic equation governing the potential. The crack cannot be neglected, b ecause it substantially alters the behavior of the potential. Numerically, it is very difficult to resolve the potential near the crack. A strategy is to treat the crack as a tower dimensional interface (hypersurface). Jump c onditions across the crack for the potential and its derivatives are necess ary for the development of numerical schemes for this approach. Besides the jump conditions, we also give an analytic example of their validity. (C) 1 999 Published by Elsevier Science Ltd. All rights reserved.