Semantic Scholar Open Access 2025 4 sitasi

Stability inequalities with explicit constants for a family of reverse Sobolev inequalities on the sphere

Tobias Konig

Abstrak

We prove a stability inequality associated to the reverse Sobolev inequality on the sphere $\mathbb S^n$, for the full admissible parameter range $s - \frac{n}{2} \in (0,1) \cup (1,2)$. To implement the classical proof of Bianchi and Egnell, we overcome the main difficulty that the underlying operator $A_{2s}$ is not positive definite. As a consequence of our analysis and recent results from Gong et al. (arXiv:2503.20350 [math.AP]), the case $s - \frac{n}{2} \in (1,2)$ remarkably constitutes the first example of a Sobolev-type stability inequality (i) whose best constant is explicit and (ii) which does not admit an optimizer.

Topik & Kata Kunci

Penulis (1)

T

Tobias Konig

Format Sitasi

Konig, T. (2025). Stability inequalities with explicit constants for a family of reverse Sobolev inequalities on the sphere. https://www.semanticscholar.org/paper/59e07ff57a4a0b8dc0bab3b5ae31fdd2b822c09d

Akses Cepat

PDF tidak tersedia langsung

Cek di sumber asli →
Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2025
Bahasa
en
Total Sitasi
Sumber Database
Semantic Scholar
Akses
Open Access ✓