The neumann problem in a plane domain bounded by closed and open curves

Abstract

The Neumann problem for the Laplace equation in a connected plane region bounded y closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.

Keywords:

• Harmonic functions
• Neumann problem:
• boundary integral equation method
• cracks

Classification Categories AMS No:

• 35J05
• 35J25

^∗ krutitskrrr miith.phys.msu.su.

^∗ krutitskrrr miith.phys.msu.su.

Notes

^∗ krutitskrrr miith.phys.msu.su.