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Published in 2021 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.107692
Abstract: We study interior $L^p$-regularity theory, also known as Calderon-Zygmund theory, of the equation \[ \int_{\mathbb{R}^n} \int_{\mathbb{R}^n} \frac{K(x,y)\ (u(x)-u(y))\, (\varphi(x)-\varphi(y))}{|x-y|^{n+2s}}\, dx\, dy = \langle f, \varphi \rangle \quad \varphi \in C_c^\infty(\mathbb{R}^n). \] For $s \in (0,1)$,…
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Keywords:
varphi;
delta;
mathbb;
int mathbb ... See more keywords
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Published in 2020 at "Turkish Journal of Mathematics"
DOI: 10.3906/mat-1907-24
Abstract: Let $W^{1,2} \mathbb{R}^2 $ be the standard Sobolev space. Denote for any real number $p>2$ \begin{align*}\lambda_{p}=\inf\limits_{u\in W^{1,2} \mathbb{R}^2 ,u\not\equiv0}\frac{\int_{\mathbb{R}^{2}} |\nabla u|^2+|u|^2 dx}{ \int_{\mathbb{R}^{2}}|u|^pdx ^{2/p}}. \end{align*} Define a norm in $W^{1,2} \mathbb{R}^2 $ by \begin{align*}\|u\|_{\alpha,p}=\left \int_{\mathbb{R}^{2}}…
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Keywords:
moser inequality;
trudinger moser;
int mathbb;
mathbb ... See more keywords