Heat kernel and resolvent properties for second order elliptic differential operators with general boundary conditions on \(L^p\) (Q2747819)
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scientific article; zbMATH DE number 1658334
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Heat kernel and resolvent properties for second order elliptic differential operators with general boundary conditions on \(L^p\) |
scientific article; zbMATH DE number 1658334 |
Statements
4 April 2003
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elliptic differential operator
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nonsmooth domains
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symmetric Markov semigroups
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ultracontractivity
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linear and semilinear parabolic equations
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Hölder continuity
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Heat kernel and resolvent properties for second order elliptic differential operators with general boundary conditions on \(L^p\) (English)
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The authors prove resolvent estimates for second order, divergence form elliptic operators under mixed boundary conditions, nonsmooth coefficients and weak assumptions of the spatial domain of arbitrary space dimension. The semigroups generated by them are analytic, map into Hölder spaces and their heat kernels are Hölder continuous in both arguments. As consequence, Hölder continuity (in space and time) is derived for the solutions to linear and semilinear parabolic equations.
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