On the variation of the fractional mean curvature under the effect of \(C^{1, \alpha}\) perturbations (Q255563)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the variation of the fractional mean curvature under the effect of \(C^{1, \alpha}\) perturbations |
scientific article; zbMATH DE number 6552525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the variation of the fractional mean curvature under the effect of \(C^{1, \alpha}\) perturbations |
scientific article; zbMATH DE number 6552525 |
Statements
On the variation of the fractional mean curvature under the effect of \(C^{1, \alpha}\) perturbations (English)
0 references
9 March 2016
0 references
The author studies how the fractional mean curvature of order \(s\in(0,1)\) varies with respect to \(C^{1,\alpha}\)-diffeomorphisms. It is proved that, if \(\alpha>s,\) then the variation of the \(s\)-mean curvature of a set \(E\) under a \(C^{1,\alpha}\)-diffeomorphism \(\Psi\) is controlled by the \(C^{0,\alpha}\)-norm of the Jacobian of \(\Psi.\) When \(\alpha=1\), the stability of these estimates is discussed as \(s\to1^-\).
0 references
fractional mean curvature
0 references
\(s\)-perimeter
0 references
fractional Laplacian
0 references
non-local equations
0 references
\(C^{1,\alpha}\)-diffeomorphism
0 references
quantitative implicit function theorem
0 references
0 references
0 references
0 references
0 references
