On some interpolation inequalities between H\"{o}lder and Lebesgue's spaces
Analysis of PDEs
2024-09-24 v1
Abstract
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.
Cite
@article{arxiv.2409.14102,
title = {On some interpolation inequalities between H\"{o}lder and Lebesgue's spaces},
author = {Sergey P. Degtyarev},
journal= {arXiv preprint arXiv:2409.14102},
year = {2024}
}