Search results for "trace theorems"

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Traces of weighted function spaces: dyadic norms and Whitney extensions

2017

The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.

Pure mathematicsTrace (linear algebra)Function spaceGeneral MathematicsDyadic cubesTriebel-Lizorkin spacesweighted Sobolev spaces01 natural sciencesfunktioanalyysiOperator (computer programming)trace theoremsClassical Analysis and ODEs (math.CA)FOS: Mathematics46E350101 mathematicsfunktioavaruudetMathematicsSmoothness (probability theory)010102 general mathematicsExtension (predicate logic)010101 applied mathematicsSobolev spacesovellettu matematiikkaMathematics - Classical Analysis and ODEsBesov spacesVariety (universal algebra)
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Solvability of a first order system in three-dimensional non-smooth domains

1985

summary:A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $\Omega\subset \bold R^3$. On the boundary $\delta\Omega$, the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

magnetostatics in vacuum [keyword]msc:65N10Friedrich’s inequality [keyword]bounded domain with Lipschitz boundary [keyword]msc:78A30boundary value problem [keyword]msc:76A02Trace theorems [keyword]msc:35Q99
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