Abstract
An exact solution for the Laplace's equation with Dirichlet boundary conditions in an arbitrary region is presented in this work. The solution is in the form of an integral in terms of the potential on the boundary, and depends on the geometry of the region. The method is valid for bounded as well as unbounded regions. Poisson's integral formula and Schwarz's integral rep resentation for the half-plane potential problem are obtained as a verification of the approach. The method also presents a generalized mean-value theorem for harmonic functions at any interior point of a circular disk in terms of weighted values at the boundary of the region.
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 callDisclaimer: 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.
