Semiclassical fundamental solutions.
Solution of the Dirichlet problem for the Laplace equation
For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.
Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier
2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.We give here examples of equations of type (1) ∂tt2 y -p(t, Dx) y = 0, where p is a singular pseudo-differential operator with regular global solutions when the Cauchy data are regular, t ∈ R, x ∈ R5.
Solutions to some nonlinear PDE's in the form of Laplace type integrals
A nonlinear equation in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.
Spectral decomposition of Green’s integrals and existence of -solutions of matrix factorizations of the Laplace operator in a ball
Spline qualocation methods for boundary integral equtions.
Steady state temperatures in a quarter plane.
Strong ellipticity of boundary integral operators.
Su una classe di equazioni paraboliche singolari