Corpus ID: 237940590

Stability of Hardy Littlewood Sobolev Inequality under Bubbling

@inproceedings{Aryan2021StabilityOH,
  title={Stability of Hardy Littlewood Sobolev Inequality under Bubbling},
  author={Shrey Aryan},
  year={2021}
}
In this note we will generalize the results deduced in arXiv:1905.08203 and arXiv:2103.15360 to fractional Sobolev spaces. In particular we will show that for $s\in (0,1)$, $n>2s$ and $\nu\in \mathbb{N}$ there exists constants $\delta = \delta(n,s,\nu)>0$ and $C=C(n,s,\nu)>0$ such that for any function $u\in \dot{H}^s(\mathbb{R}^n)$ satisfying, \begin{align*} \left\| u-\sum_{i=1}^{\nu} \tilde{U}_{i}\right\|_{\dot{H}^s} \leq \delta \end{align*} where $\tilde{U}_{1}, \tilde{U}_{2},\cdots \tilde{U… Expand

References

SHOWING 1-9 OF 9 REFERENCES
On the Sharp Stability of Critical Points of the Sobolev Inequality
Given $$n\ge 3$$ n ≥ 3 , consider the critical elliptic equation $$\Delta u + u^{2^*-1}=0$$ Δ u + u 2 ∗ - 1 = 0 in $${\mathbb {R}}^n$$ R n with $$u > 0$$ u > 0 . This equation corresponds to theExpand
Sharp quantitative estimates of Struwe's Decomposition
Suppose u ∈ Ḣ(R). In a fundamental paper [17], Struwe proved that if u ≥ 0 and ||∆u + u n+2 n−2 ||H−1 := Γ(u) → 0 then δ(u) → 0, where δ(u) denotes the Ḣ(R)-distance of u from the manifold of sums ofExpand
Best constant in Sobolev inequality
SummaryThe best constant for the simplest Sobolev inequality is exhibited. The proof is accomplished by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculusExpand
Functional Spaces for the Theory of Elliptic Partial Differential Equations
Preliminaries on ellipticity.- Notions from Topology and Functional Analysis.- Sobolev Spaces and Embedding Theorems.- Traces of Functions on Sobolev Spaces.- Fractional Sobolev Spaces.- EllipticExpand
Non degeneracy of the bubble in the critical case for non local equations
We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian.
Fractional Laplace operator and its properties
Explicit expression for the fractional laplacian of 1/(1 + |x| 2 ) s . MathOverflow
    Release 1.1.2 of 2021-06-15