The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are Hölder continuous with respect to space variables (Q1357123)
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scientific article; zbMATH DE number 1022351
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are Hölder continuous with respect to space variables |
scientific article; zbMATH DE number 1022351 |
Statements
The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are Hölder continuous with respect to space variables (English)
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20 July 1997
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Summary: We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution \(u\) which is bounded with values in \(C^{2+ \theta} (\overline\Omega)\) \((0< \theta<1)\), with \(\partial_tu\) bounded with values in \(C^\theta (\overline\Omega)\).
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analytic semigroup
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maximal regularity
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strict solution
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