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2017

Embeddings for $\mathbb{A}$-weakly differentiable functions on domains

Gmeineder, Franz, Raiţă, Bogdan

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We prove that the critical embedding $\mathrm{W}^{\mathbb{A},1}(B)\hookrightarrow \mathrm{W}^{k-1,\frac{n}{n-1}}$ holds if and only if the $k$-homogeneous, linear differential operator $\mathbb{A}$ on $\mathbb{R}^n$ from $\mathbb{R}^N$ to $\mathbb{R}^m$ has finite dimensional null-space.

Here $B$ is a ball in $\mathbb{R}^n$ and $\mathrm{W}^{\mathbb{A},1}(B)$ denotes the space of maps $u\in \mathrm{L}^1(B,\mathbb{R}^N)$ such that the vector valued distribution $\mathbb{A}u$ is an integrable map.
The result was previously known only for several examples of $\mathbb{A}$.
Our result contrasts the homogeneous embedding in full-space.

Embeddings for $\mathbb{A}$-weakly differentiable functions on domains · Around

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Whitney, H
1934
Earlier work this paper cites.
Sobolev, S.L
1938
Earlier work this paper cites.
Calderón, A.P
1952
Earlier work this paper cites.
Lopatinskiĭ, Y.B
1953
Earlier work this paper cites.
Aronszajn, N
1954
Earlier work this paper cites.
Gagliardo, E
1958
Earlier work this paper cites.
Agmon, S
1959
Earlier work this paper cites.
Nirenberg, L
1959
Earlier work this paper cites.
Smith, K.T
1961
Earlier work this paper cites.
Uspenskiĭ, S.V
1961
Earlier work this paper cites.
Ornstein, D
1962
Earlier work this paper cites.
Agmon, S
1964
Earlier work this paper cites.
Hörmander, L
1966
Earlier work this paper cites.
Reshetnyak, Y.G
1970
Earlier work this paper cites.
Smith, K.T
1970
Earlier work this paper cites.
Strauss, M.J
1973
Earlier work this paper cites.
Peetre, J
1979
Earlier work this paper cites.
Suquet, P.M
1979
Earlier work this paper cites.
Strang, G
1980
Earlier work this paper cites.
Jones, P.W
1981
Earlier work this paper cites.

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