Multiplicative Inequalities for Derivatives, and a Priori Estimates of Smoothness of Solutions of Nonlinear Differential Equations

Abstract

Inequalities of the following form are proved: if is an arbitrary function and , then where depends only on . The exponent is a limiting exponent. With the inequalities as a basis, imbedding theorems are constructed for classes of solutions of nonlinear singular differential equations in the space of times differentiable functions.