Two results relating an \(L^p\) regularity condition and the \(L^q\) Dirichlet problem for parabolic equations (Q2291836)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two results relating an \(L^p\) regularity condition and the \(L^q\) Dirichlet problem for parabolic equations |
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Two results relating an \(L^p\) regularity condition and the \(L^q\) Dirichlet problem for parabolic equations (English)
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31 January 2020
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The authors discuss the solvability of the linear second order parabolic equation \[ \partial_t u(x,t)-\operatorname{div}(A(x)\nabla u(x,t))=0 \] in the set of Lipschitz cylinders, where \(A\) is symmetric and uniformly elliptic matrix. \(L^p\) regularity of solution in the presence of \(L^q\) Dirichlet boundary condition is also discussed.
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initial \(L^p\) Dirichlet problem
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initial \(L^q\) regularity problem
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Lipschitz cylinder
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