On Fundamental Solutions of Generalized Schrödinger Operators

On Fundamental Solutions of Generalized Schrödinger Operators

We consider the generalized Schrr odinger operator ? + where is a nonnegative Radon measure in R n , n 3. Assuming that satisses certain scale-invariant Kato condition and doubling condition, we establish the following bounds for the fundamental solution of ? + in R n : where d(x; y;) is the distance function for the modiied Agmon metric m(x;)dx 2 associated with. We also study the boundedness ...

Fundamental Solutions of Dynamic Poroelasticity and Generalized Termoelasticity

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

Fundamental Solutions: Ii-matrix Operators

In this tutorial, we will continue the discussion, started in the tutorial 4, about the derivation of the fundamental solutions. In the former tutorial, we presented techniques for setting up the fundamental solution for simple and compound operators. Herein, we will discuss the use of operator decoupling technique to breakdown matrix operators to simple or compound scalar ones. This method is ...

Fundamental Solutions of Cubic Operators In

Fundamental Solutions: I-simple and Compound Operators

In the tutorial 3, we presented other examples on the derivation of the boundary integral equation in the direct form. Mainly, elasticity and plate in bending problems were discussed. In this tutorial, we will discuss the definitions and the methods of derivation of fundamental solutions. The use of such solution within the boundary element method was discussed in the former tutorial. A table p...