Variational treatment of electrostatic interaction force in atomic force microscopy (Q957851)

The authors discuss a computational method which allows the authors to determine the electrostatic interaction force between an atomic force microscope tip and the sample surface. After formulating the corresponding boundary value problem in a Sobolev space setting, the authors find the weak solution in the form of the integral potential. In the last part of the paper, this solution is approximated numerically using generalized Fourier series to make it applicable for practical computations.