Can somebody provide some intuitive reasoning why in higher dimensions can functions in Sobolev spaces be discontinuous? It is clear in 1D why a discontinuous function cannot be in a Sobolev space (by working out), but how does that work out in higher dimensions. And, what kinds of discontinuities are allowable. Thanks, Sandy.
2026-05-13 18:29:20.1778696960
Discontinuous functions in Sobolev Spaces
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