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LSpice
LSpice
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On the first page of anthe old paper paperSolution of Bogovskiithe first boundary value problem for an equation of continuity of an incompressible medium of Bogovskii, the notationnotations $W_p^l(\Omega)$ and $L_p^l(\Omega)$ isare used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L_p(\Omega) := \{ f : \Omega \to \mathbb{R} : f \textrm{ is measurable and } \int_{\Omega} |f|^p < \infty \}$ whose weak derivatives of order up to $l$ are also in $L_p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?

On the first page of an old paper of Bogovskii, the notation $W_p^l(\Omega)$ and $L_p^l(\Omega)$ is used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L_p(\Omega) := \{ f : \Omega \to \mathbb{R} : f \textrm{ is measurable and } \int_{\Omega} |f|^p < \infty \}$ whose weak derivatives of order up to $l$ are also in $L_p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?

On the first page of the old paper Solution of the first boundary value problem for an equation of continuity of an incompressible medium of Bogovskii, the notations $W_p^l(\Omega)$ and $L_p^l(\Omega)$ are used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L_p(\Omega) := \{ f : \Omega \to \mathbb{R} : f \textrm{ is measurable and } \int_{\Omega} |f|^p < \infty \}$ whose weak derivatives of order up to $l$ are also in $L_p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?

clarify notation for $L_p$ spaces
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A guy
A guy
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On the first page of an old paper of Bogovskii, the notation $W_p^l(\Omega)$ and $L_p^l(\Omega)$ is used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L^p(\Omega)$$L_p(\Omega) := \{ f : \Omega \to \mathbb{R} : f \textrm{ is measurable and } \int_{\Omega} |f|^p < \infty \}$ whose weak derivatives of order up to $l$ are also in $L^p(\Omega)$$L_p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?

On the first page of an old paper of Bogovskii, the notation $W_p^l(\Omega)$ and $L_p^l(\Omega)$ is used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L^p(\Omega)$ whose weak derivatives of order up to $l$ are also in $L^p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?

On the first page of an old paper of Bogovskii, the notation $W_p^l(\Omega)$ and $L_p^l(\Omega)$ is used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L_p(\Omega) := \{ f : \Omega \to \mathbb{R} : f \textrm{ is measurable and } \int_{\Omega} |f|^p < \infty \}$ whose weak derivatives of order up to $l$ are also in $L_p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?

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A guy
A guy
  • 13
  • 3

The meaning of $L_p^l(\Omega)$ in a paper of Bogovskii on Sobolev spaces

On the first page of an old paper of Bogovskii, the notation $W_p^l(\Omega)$ and $L_p^l(\Omega)$ is used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L^p(\Omega)$ whose weak derivatives of order up to $l$ are also in $L^p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?