Interface Oblique Derivative Problem for Perturbed \(p(x)\) -Laplacian Equation in a Bounded n-Dimensional Cone

The aim of this chapter is the investigation of the behavior of the weak solutions to the interface oblique derivative problem for the perturbed variable \(p(x)\) -Laplacian in a neighborhood of a conical boundary point of the bounded n-dimensional cone ( \(n\geq 2\) ). The interface problems appear frequently in various areas of physics and technics. For instance, one of the important problems of the electrodynamics of solid media is the research of electromagnetic processes in ferromagnetic with various dielectric constants.