arXiv:2409.14102 Abstract | arXiv Analytics

arXiv:2409.14102 [math.AP]Abstract References Reviews Resources

On some interpolation inequalities between Hölder and Lebesgue's spaces

Published 2024-09-21Version 1

We present a simple proof of some interpolation inequalities between H\"{o}lder 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\"{o}lder class for a solution to some quasilinear parabolic initial boundary value problem.

Categories: math.AP

Subjects: 26D10, 35K59

Keywords: interpolation inequalities, lebesgues spaces, parabolic initial boundary value problem, quasilinear parabolic initial boundary value, simple proof

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