A Note on the Jump Conditions for Systems of Conservation Laws - Srinivasan, G. K.; Sharma, V. D. (Studies in applied mathematics (Cambridge), 2003)
In [1], the authors have demonstrated the effect on the Rankine–Hugoniot conditions for a system of conservation laws driven by a singular forcing function and have applied their results to a problem in water waves. We analyze here a similar problem in several space dimensions, in which the singularity in the forcing term involves a simple layer potential supported along the singularity locus. A classical theorem in electrostatics appears as a special case.