The heat equation in \(L_{q}((0,T),L_{p})\)-spaces with weights (Q2706227)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The heat equation in \(L_{q}((0,T),L_{p})\)-spaces with weights |
scientific article |
Statements
19 March 2001
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bounded measurable coefficients
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blow up near the boundary
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The heat equation in \(L_{q}((0,T),L_{p})\)-spaces with weights (English)
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The author studies the following uniformly parabolic equation NEWLINE\[NEWLINE u_t(t,x)=a^{ij}(t)u_{x^ix^j}(t,x) +f(t,x) NEWLINE\]NEWLINE in several subdomains of \(\mathbb{R}\times\mathbb{R}^d=\{(t,x):t\in\mathbb{R}\), \(x\in\mathbb{R}^d\}\) with \(a^{ij}\) being only bounded measurable functions of \(t.\) There are presented existence and uniqueness results in \(L_p\)-spaces with or without weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.
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