Class Of Well-posed Problems Research Articles

On regularized trace formulas for a well-posed perturbation of the m-Laplace operator

A class of well-posed problems in a Hilbert space for the m-Laplace operator in a punctured domain is considered. An analog of the Green formula and a class of self-adjoint problems are obtained. We derive regularized trace formulas for these operators.

Laplace operator with δ-like potentials

We study the Laplace operator in a punctured domain in a Hilbert space. We obtain an analog of the Green formula and a class of self-adjoint extensions of the Laplacian. We also investigate a certain class of well-posed problems.

Numerical solution of the reduction problem when the ratio of the half-widths of the slit function and the observed contour is close to unity

The question of obtaining a solution that is stable in the presence of initialdata error for the reduction problem in Raman scattering for various ratios of the half-widths of the slit function and the observed contour is discussed. It is shown that when the ratio of the half-widths is close to unity, a stable solution in the class of well-posed problems can be obtained by application of the discrete Fourier transform.