Boundary-Value Problem for Nonuniformly Elliptic Equations with Power Singularities - Pukalsky, Ivan; Luste, Iryna (Journal of Mathematical Sciences, 2024)
By using a priori estimates and the Riesz theorem, we investigate a boundary-value problem for nonuniformly 2b -elliptic equations with arbitrary power singularities in the coefficients of the equation and boundary conditions on a certain set of points. We establish the existence and obtain an integral representation of the unique solution of the formulated boundary-value problem in Hölder spaces with power weights whose order is determined via the orders of singularities in the coefficients of the equation and boundary conditions.
Keywords: boundary-value problem; power singularities; interpolation inequalities; Hölder spaces; Arzelà theorem; Riesz theorem; Borel measure