Title: The continuity of functions with N-th derivative measure
Abstract:We study the continuity of functions u whose mixed derivative partial derivative 1...partial derivative(Nu) is a measure. If u epsilon W-1,W-1(R-N), then we prove that u is continuous. The same conclu...We study the continuity of functions u whose mixed derivative partial derivative 1...partial derivative(Nu) is a measure. If u epsilon W-1,W-1(R-N), then we prove that u is continuous. The same conclusion holds for u epsilon W-k,W-p(Q), with kp > N - 1, where Q denotes a cube in R-N. The key step in the proof consists in showing that the measure partial derivative(1)...partial derivative(Nu) does not charge hyperplanes orthogonal to the coordinate axes.Read More
Publication Year: 2007
Publication Date: 2007-01-01
Language: en
Type: article
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Cited By Count: 8
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