A Laplace type problems for a lattice with cell composed by three quadrilaterals and with maximum probability

Abstract

In some previous papers [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10] the authors studies same Laplace problems with different fundamental cells. In this paper we consider a lattice with cell represented as in figure 1 and we compute the probability that a segment of random position and constant length intersects a side of lattice. Then we prove that there are values for parameters that determine the lattice and the length of segment for which the probability determined is maximum.