The continuity of functions with N-th derivative measure
(2007) Houston Journal of Mathematics — Vol. 33, n° 3, p. 927-939 (2007)
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- Abstract
- (en) 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.
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Ponce, A., & Van Schaftingen, J. (2007). The continuity of functions with N-th derivative measure. Houston Journal of Mathematics, 33(3), 927-939. https://hdl.handle.net/2078.5/246368 (Original work published 2007)