\(L_p\)-Estimates for solutions to the Dirichlet and Neumann problems for the heat equation in a wedge with edge of arbitrary codimension (Q2773603)
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scientific article; zbMATH DE number 1710234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L_p\)-Estimates for solutions to the Dirichlet and Neumann problems for the heat equation in a wedge with edge of arbitrary codimension |
scientific article; zbMATH DE number 1710234 |
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24 February 2002
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estimates for Green functions
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anisotropic Kondrat'ev spaces
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boundary with singular points
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\(L_p\)-Estimates for solutions to the Dirichlet and Neumann problems for the heat equation in a wedge with edge of arbitrary codimension (English)
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The author presents new results on the \(L_p\)-theory of boundary value problems for parabolic equations in domains with singularities in the case of \(p\neq 2\). A particular attention is paid to the heat equation in a wedge with edge of arbitrary codimension. Using estimates for Green functions to boundary value problems in a cone, the author obtains a priori estimates for solutions to the Dirichlet and Neumann problems in a wedge with edge of arbitrary codimension. In addition, the so-called coercive estimates for solutions are exposed in anisotropic Kondrat'ev spaces.
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