\(BV\) functions and parabolic initial boundary value problems on domains (Q731395)
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scientific article; zbMATH DE number 5610627
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(BV\) functions and parabolic initial boundary value problems on domains |
scientific article; zbMATH DE number 5610627 |
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\(BV\) functions and parabolic initial boundary value problems on domains (English)
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2 October 2009
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The authors consider semigroup \((T(t))_{t\geq 0}\) generated by a uniformly elliptic second order operator \(A\) in \(L^1(\Omega)\) under homogeneous co-normal boundary conditions on \(\partial\Omega.\) It is shown that the limit as \(t\to 0\) of the \(L^1\)-norm of \(D_x T(t)u_0\) tends to the total variation of the initial datum \(u_0,\) and in particular is finite if and only if \(u_0\) belongs to \(BV(\Omega)\) or weighted \(BV\) spaces.
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linear parabolic equations
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BV functions
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semigroup theory
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