I want to know the difference between single layer and double layer potentials. Is there a link between the choice of single/double layer potential and the boundary condition of a PDE or an homogeneity?
2026-03-28 23:57:26.1774742246
What is the difference between single and double layer potential
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Single layer potential is continuous on the boundary, but its normal derivative jumps by a specified amount as we cross the boundary. This property can be used to solve the Neumann problem (prescribed normal derivative on the boundary).
Double layer potential is itself discontinuous on the boundary, its value jumps by a specified amount as we cross the boundary. This property can be used to solve the Dirichlet problem (prescribed boundary values).
The passage from the jump properties to the solution of boundary problem takes some work. This topic is discussed in much detail on Wikipedia: Neumann–Poincaré operator and on EoM: Potential theory.