4 papers
Perturbations of the Dirichlet Problem and Error Bounds
Charles Z. Martin
The Dirichlet problem on a bounded planar domain is more readily understood and solved for the Laplace operator than it is for a Schrodinger operator. When the potential function i…
Variational Methods and Planar Elliptic Growth
Charles Z. Martin
A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the…
Variation of Green Functions: Normal Derivatives
Charles Z. Martin
We derive a variational formula for the outward normal derivative of the Green function for the Schrödinger and Laplace--Beltrami operators, viewed as perturbations of the Laplacia…
Variational Formulas for the Green Function
Charles Z. Martin
The Green function has a complex dependence upon its underlying domain and differential operator. We briefly review Hadamard's formula for the first variation of the Green function…