A weighted \(L_p\)-theory for divergence type parabolic PDEs with BMO coefficients on \(C^1\)-domains (Q2019143)
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scientific article; zbMATH DE number 6420107
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A weighted \(L_p\)-theory for divergence type parabolic PDEs with BMO coefficients on \(C^1\)-domains |
scientific article; zbMATH DE number 6420107 |
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A weighted \(L_p\)-theory for divergence type parabolic PDEs with BMO coefficients on \(C^1\)-domains (English)
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27 March 2015
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The authors present a weighted \(L^p\)-theory of parabolic equations of divergence type of the form \[ u_t=(a^{ij}(t,x)u_{x^j}+b^i(t,x)u+f^i)_{x^j}+ \bar{b}_i(t,x)u_{x^i} + c(t,x)u+g \] defined on \(C^1\) domains. The leading coefficients have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation), and the lower-order coefficients are allowed to be unbounded and to blow up near the boundary.
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parabolic equations of divergence type
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weighted Sobolev spaces
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\(L^p\)-theory
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BMO coefficients
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VMO coefficients
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