On a scale of anisotropic Sobolev spaces
with Ian Tice · Communications on Pure and Applied Analysis
Analysis of PDEs
Functional Analysis
Subhasish Mukherjee and Ian Tice. “On a scale of anisotropic Sobolev spaces.” Communications on Pure and Applied Analysis 23 (2024), no. 9, 1240–1260.
arXiv:2312.06044 · Journal (DOI: 10.3934/cpaa.2024055) · PDF
Abstract
We introduce a scale of anisotropic Sobolev spaces defined through a three-parameter family of Fourier multipliers and study their functional analytic properties. These spaces arise naturally in PDE when studying traveling wave solutions, and we give some simple applications of the spaces in this direction.