Concretization of formulas for regularized trace of the Laplace operator power with potential on right-angled isosceles triangle
We represent several formulas for the ﬁrst regularized trace of any power α > 1 of the Laplace operator on a right-angled isosceles triangle with mixed boundary conditions and a measurable essen- tially bounded potential. On every side of the triangle either the Dirichlet boundary condition or the Neumann boundary condition are given; the Dirichlet boundary problem and the Neumann boundary problem are particular cases of mixed boundary conditions. The trace formulas are rended concrete for suﬃciently large classes of potentials and are improved for powers α > 96/73.