Zobrazeno 1 - 10
of 230
pro vyhledávání: '"Koenig, Tobias"'
Under appropriate positivity hypotheses, we prove quantitative estimates for the total $k$-th order $Q$-curvature functional near minimizing metrics on any smooth, closed $n$-dimensional Riemannian manifold for every integer $1 \leq k < \frac{n}{2}$.
Externí odkaz:
http://arxiv.org/abs/2407.06934
The fractional Caffarelli-Kohn-Nirenberg inequality states that $$ \int_{\mathbb{R}^n}\int_{\mathbb{R}^n} \frac{(u(x)-u(y))^2}{|x|^\alpha |x-y|^{n+2s} |y|^\alpha} \mathrm{d} x \, \mathrm{d} y \geq \Lambda_{n, s, p, \alpha,\beta} \|u |x|^{-\beta}\|_{L
Externí odkaz:
http://arxiv.org/abs/2403.02303
Autor:
König, Tobias
In this paper, for $d \geq 1$ and $s \in (0,\frac{d}{2})$, we study the Bianchi-Egnell quotient \[ \mathcal Q(f) = \inf_{f \in \dot{H}^s(\mathbb R^d) \setminus \mathcal B} \frac{\|(-\Delta)^{s/2} f\|_{L^2(\mathbb R^d)}^2 - S_{d,s} \|f\|_{L^{\frac{2d}
Externí odkaz:
http://arxiv.org/abs/2308.16794
Autor:
König, Tobias
We prove that the stability inequality associated to Sobolev's inequality and its set of optimizers $\mathcal M$ and given by \[ \frac{\|\nabla f\|_{L^2(\mathbb R^d)}^2 - S_d \|f\|_{L^\frac{2d}{d-2}(\mathbb R^d)}^2}{ \inf_{h \in \mathcal M} \|\nabla
Externí odkaz:
http://arxiv.org/abs/2211.14185
Autor:
De Nitti, Nicola, König, Tobias
We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function $u \in \dot H^s(\mathbb R^N)$ whose energy satisfies $$\tfrac{1}{2} S^\frac{N}{2s}_{N,s} \le \|u\|_{\dot H^s(\mathb
Externí odkaz:
http://arxiv.org/abs/2211.10634
Autor:
König, Tobias, Laurain, Paul
For a bounded set $\Omega \subset \mathbb R^N$ and a perturbation $V \in C^1(\overline{\Omega})$, we analyze the concentration behavior of a blow-up sequence of positive solutions to \[ -\Delta u_\epsilon + \epsilon V = N(N-2) u_\epsilon^\frac{N+2}{N
Externí odkaz:
http://arxiv.org/abs/2211.00595
Autor:
König, Tobias
This note is concerned with the Bianchi-Egnell inequality, which quantifies the stability of the Sobolev inequality, and its generalization to fractional exponents $s \in (0, \frac{d}{2})$. We prove that in dimension $d \geq 2$ the best constant \[ c
Externí odkaz:
http://arxiv.org/abs/2210.08482
Autor:
König, Tobias, Wang, Yamin
Publikováno v:
Nonlinear Analysis, Vol. 232, July 2023, 113253
We study singular metrics of constant negative $Q$-curvature in the Euclidean space $\mathbb{R}^n$ for every $n \geq 1$. Precisely, we consider solutions to the problem \[ (-\Delta)^{n/2}u=-e^{nu}\quad \text{on}\quad\mathbb{R}^{n}\backslash \{0\}, \]
Externí odkaz:
http://arxiv.org/abs/2209.00883
Autor:
König, Tobias, Laurain, Paul
For a smooth bounded domain $\Omega \subset \mathbb R^3$ and smooth functions $a$ and $V$, we consider the asymptotic behavior of a sequence of positive solutions $u_\epsilon$ to $-\Delta u_\epsilon + (a+\epsilon V) u_\epsilon = u_\epsilon^5$ on $\Om
Externí odkaz:
http://arxiv.org/abs/2208.12337
Autor:
König, Tobias
Publikováno v:
In Journal of International Money and Finance October 2024 148