Cargando…
Sharp Sobolev Inequalities via Projection Averages
A family of sharp [Formula: see text] Sobolev inequalities is established by averaging the length of i-dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical [Formula: see text] Sobolev inequality of Aubin and...
Autores principales: | , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2020
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8549948/ https://www.ncbi.nlm.nih.gov/pubmed/34720562 http://dx.doi.org/10.1007/s12220-020-00544-6 |
Sumario: | A family of sharp [Formula: see text] Sobolev inequalities is established by averaging the length of i-dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical [Formula: see text] Sobolev inequality of Aubin and Talenti and that the strongest member of this family is the only affine invariant one among them—the affine [Formula: see text] Sobolev inequality of Lutwak, Yang, and Zhang. When [Formula: see text] , the entire family of new Sobolev inequalities is extended to functions of bounded variation to also allow for a complete classification of all extremal functions in this case. |
---|