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Francesco Polizzi
Francesco Polizzi
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Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev embedding theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

Question. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev embedding theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev embedding theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous.

Question. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

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YCor
YCor
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Sobolev Embeddingembedding for fractional Sobolev Spacesspaces

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev Embedding Theoremembedding theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

Sobolev Embedding for fractional Sobolev Spaces

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev Embedding Theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

Sobolev embedding for fractional Sobolev spaces

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev embedding theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

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Nirav
Nirav
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Sobolev Embedding for fractional Sobolev Spaces

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev Embedding Theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?