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Nonuniform Sobolev Spaces
- Publication Year :
- 2024
-
Abstract
- We study nonuniform Sobolev spaces, i.e., spaces of functions whose partial derivatives lie in possibly different Lebesgue spaces. Although standard proofs do not apply, we show that nonuniform Sobolev spaces share similar properties as the classical ones. These spaces arise naturally in the study of certain PDEs. For instance, we illustrate that nonuniform fractional Sobolev spaces are useful in the study of local estimates for solutions of heat equations and the convergence of Schr\"odinger operators. In this work we extend recent advances on local energy estimates for solutions of heat equations and the convergence of Schr\"odinger operators to nonuniform fractional Sobolev spaces.<br />Comment: 42 pages
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2401.02856
- Document Type :
- Working Paper