On the Hölder property of one elliptic equation
The paper deals with an elliptic in the unit disk equation of the divergence form with discontinuity lines coinciding with the two-dimensional coordinate system axes. On the above lines it has the order degeneration in the second and forth quadrants as a power function of the radius of the order \(\alpha\) and with the order \(-\alpha\), \(0<\alpha<2\), in the first and third quadrants. Introducing in the natural way classes of generalized solutions in the corresponding weighted Sobolev space, the Hölder property of the solutions of the equation under consideration is studied.
scientific article; zbMATH DE number 5000619
scientific article