A counterexample to the Lp-Hodge decomposition
Hajłasz, Piotr
Banach Center Publications, Tome 37 (1996), p. 79-83 / Harvested from The Polish Digital Mathematics Library
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We construct a bounded domain Ω⊂ℝ2 with the cone property and a harmonic function on Ω which belongs to W01,p(Ω) for all 1 ≤ p < 4/3. As a corollary we deduce that there is no Lp-Hodge decomposition in Lp(Ω,ℝ2) for all p > 4 and that the Dirichlet problem for the Laplace equation cannot be in general solved with the boundary data in W1,p(Ω) for all p > 4.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:262838 
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     author = {Haj\l asz, Piotr},
     title = {A counterexample to the $L^{p}$-Hodge decomposition},
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {79-83},
     zbl = {0846.35035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p79bwm}
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Hajłasz, Piotr. A counterexample to the $L^{p}$-Hodge decomposition. Banach Center Publications, Tome 37 (1996) pp. 79-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p79bwm/

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