Multiple Laplace integral

On Laplace ' S Integral Equations

which is known in the literature as Laplace's integral equation. The contour (C) and the function f(z) are supposed given and F(x) is to be found. In the case when the contour (C) consists of the positive part of the axis of reals, the solution of the equation (*■) was given by H. Poincaré t and H. Hamburger. % Each of these authors considers F(x) as a function of the real variable *. When the ...

Laplace Transform Using the Henstock-kurzweil Integral

We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.

Preliminary Note on the Inversion of the Laplace Integral.

uniformly for 0 < t < c. This result was obtained earlier by E. Post2 under the restriction of continuity on sp(t) but without the condition that p(t) approaches a limit as t becomes infinite. On the other hand the uniformity of the approach was not obtained by Post. In the present note we sketch a theory whereby the integral equation (1) may be solved with no restriction on so(t) as to continu...

Boundary Integral Equations for the Laplace–Beltrami Operator

Fast Laplace Solver by Boundary Integral Based Domain Decomposition Methods

A new method called Boundary Integral-based Domain Decomposition is proposed for the fast solution of the Laplace equation on regular and irregular regions. The idea of the method is to adopt the domain decomposition approach by partitioning into subdomains and use an integral equation formulation to compute the interface values. The method provides a particularly eecient algorithm for parallel...