The method of layer potentials is one of the classical approaches to solving boundary value problems for (strongly) elliptic equations. This method reduces the original problem to that of inverting an operator of the form "1/2 +K" on appropriate boundary function spaces. Recently, this method has attacted considerable attention both in the theoretical and the applied mathematics. This dissertation deals with the method of layer potentials on domains with conical points from a groupoid point of view. By a desingularization process and integration of a Lie algebroid, we can construct a Lie...

The method of layer potentials is one of the classical approaches to solving boundary value problems for elliptic differential equations. This method reduces the original problem to that of inverting an operator of the form '1/2+K' on appropriate function spaces on the boundary. If the boundary is smooth, then the double-layer potential operator K is compact; hence, '1/2+K' is Fredholm of index zero. However, if the boundary is non-smooth, the operator K is no longer compact. This book delves into the method of layer potentials on certain domains with singularities from a groupoid...