English

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.

Keywords

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}
}