Minimization of elliptic non-local functionals involving \(\vec{p}(\cdot)\)-Laplacian (Q6156228)
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scientific article; zbMATH DE number 7695143
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimization of elliptic non-local functionals involving \(\vec{p}(\cdot)\)-Laplacian |
scientific article; zbMATH DE number 7695143 |
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Minimization of elliptic non-local functionals involving \(\vec{p}(\cdot)\)-Laplacian (English)
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13 June 2023
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The authors show existence results for certain non-local elliptic problems involving a Laplacian \(\Delta_{\vec{p}(.)}\) with a variable exponent which generalizes the \(p\)-Laplacian \(\Delta_p u=\operatorname{div}(|\nabla u^{p-2}\nabla u)\). In the proof a concentration compactness result is used.
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\(\vec{p}(\cdot)\)-Laplacian
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concentration-compactness principle
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anisotropic variable exponent Sobolev spaces
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constrained minimization
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