Distributional Derivatives of Functions with Jump Discontinuities
In boundary and initial-value problems relating to the potential, scattering and wave propagation theories, we encounter functions that are defined inside or outside some surface S if the surface is closed, and on both sides of it if it is open. However, these functions or their first- or higher-order derivatives have jumps across 5. Classical theory is based on solving such problems on both sides of the boundaries and then attempting to satisfy the boundary conditions or jump conditions across S, as the case may be. There are many problems, however, that cannot be solved by classical techniques.
KeywordsJump Discontinuity Vortex Sheet Biharmonic Equation Distributional Derivative Biharmonic Operator
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