Abstract

The mixed Dirichlet-Neumann problem for the Laplace equation in an unbounded plane domain with cuts (cracks) is studied. The Dirichlet condition is given on closed curves making up the boundary of the domain, while the Neumann condition is specified on the cuts. The existence of a classical solution is proved by potential theory and a boundary integral equation method. The integral representation for a solution is obtained in the form of potentials. The density of the potentials satisfies a uniquely solvable Fredholm integral equation of the second kind and index zero. Singularities of the gradient of the solution at the tips of the cuts are investigated.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.