On some interpolation inequalities between H\"older and Lebesgue's spaces
Abstract
We present a simple proof of some interpolation inequalities between H\"older and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate in a smooth H\"older class for a solution to some quasilinear parabolic initial boundary value problem.
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