The Dirichlet problem for the Laplace equation in a starlike domain

Many applications of Mathematical Physics and Engineering are connected with the Laplacian, however, the most part of BVP relevant to the Laplacian are solved in explicit form only for domains with a very special shape, namely intervals, cylinders or domains with particular (circular or spherical) symmetries [1]. In recent articles (see [2], [3], [4], [5]) a solution of the Dirichlet problem for the Laplace equation in two and three-dimensional starlike domains (i.e. domains which are normal with respect to a suitable polar or spherical co-ordinate system) was achieved by using classical methods. Different techniques was also used for solving this problem, both by theoretical or numerical approaches. The relevant literature is quite extensive, mainly in Russian language (see e.g. [6], [7], [8], [9], [10], [11], [12]), however, none of the above mentioned articles is connected with the approach we have considered, which traces back to the original Fourier method. In this survey we show...

• Type: Conference
• Year: 2008
• Where: CSC
• Authors: Diego Caratelli, Paolo Emilio Ricci
• Keywords: Applied Computing, CSC 2008, Dirichlet Problem, Starlike Domains, Three-dimensional Starlike Domains