9 problems

Let $d\geq 2$, let $s>0$, and set $1/\tau=s/(d-1)$. The relevant approximation error is measured in the Triebel–Lizorkin space $\mathcal{F}^{0q}_\infty(\mathbb{S}^{d-1})$ using non…

The paper considers the hyperbolic Keller–Segel system with time-dependent parameters and its global strong solutions in the critical Besov space…

Let $A^{s,\tau}_{p,q}(\mathbb{R}^n)$ denote either a Besov-type or Triebel--Lizorkin-type space, with $s>0$, $p,q\in[1,\infty]$ (and $p<\infty$ in the Triebel--Lizorkin case), and…

Let $A = \operatorname{diag}(2^{a_1},\ldots,2^{a_d})$ and $B = \operatorname{diag}(2^{b_1},\ldots,2^{b_d})$ be diagonal matrices with anisotropies…

Let $D=\mathbb{R}^d\setminus\mathbb{R}^{\ell}$ with $0\leq\ell<d$, and let $\sigma_{\tau,2}=d\left(\frac{1}{\min(1,\tau)}-1\right)$. The refined localization space…

Triebel–Lizorkin Sobolev characterization conjecture. The two seminorms are equivalent under the stated hypotheses, with constants depending only on $s,p,q,n$.

Let $0<s<\infty$, $s\notin {\mathbb N}$, let $1\leq p<\infty$, $1\leq q\leq\infty$, and let $d\in\mathbb N$. Suppose that $\Omega_1,\Omega_2\subset\mathbb R^d$ are uniform domains,…

Let $s\in\mathbb{R}$, write $s=n_s+\{s\}$ with $n_s\in\mathbb{Z}$ and $0<\{s\}\leq 1$, and let $\Omega$ be a bounded $F^{s+1-1/p}_{p,p}$-domain for some $2<p\{s\}<\infty$. Let…

Let $0<s<2$ and $1<p<\infty$ satisfy $s<\frac{2}{p}$. Let $\mu,\nu\in F^s_{p,q}\cap L^\infty_c$ satisfy the ellipticity condition, and let $f$ be the principal solution to the Belt…