Maximal L p -regularity for the Laplacian on Lipschitz domains


Show simple item record Wood, Ian 2007-11-06T09:59:25Z 2007-11-06T09:59:25Z 2007-04
dc.identifier.citation Wood , I 2007 , ' Maximal L p -regularity for the Laplacian on Lipschitz domains ' Mathematische Zeitschrift , vol 255 , no. 4 , pp. 855-875 . , 10.1007/s00209-006-0055-6 en
dc.identifier.issn 0025-5874
dc.identifier.other PURE: 72925
dc.identifier.other dspace: 2160/348
dc.identifier.uri en
dc.description I.Wood: Maximal Lp-regularity for the Laplacian on Lipschitz domains, Math. Z., 255, 4 (2007), 855-875. en
dc.description.abstract We consider the Laplacian with Dirichlet or Neumann boundary conditions on bounded Lipschitz domains Ω, both with the following two domains of definition: D1(Δ)={u∈W1,p(Ω):Δu∈Lp(Ω), Bu=0} , or D2(Δ)={u∈W2,p(Ω):Bu=0} , where B is the boundary operator. We prove that, under certain restrictions on the range of p, these operators generate positive analytic contraction semigroups on L p (Ω) which implies maximal regularity for the corresponding Cauchy problems. In particular, if Ω is bounded and convex and 1<p≤2 , the Laplacian with domain D 2(Δ) has the maximal regularity property, as in the case of smooth domains. In the last part, we construct an example that proves that, in general, the Dirichlet–Laplacian with domain D 1(Δ) is not even a closed operator. en
dc.format.extent 21 en
dc.language.iso eng
dc.relation.ispartof Mathematische Zeitschrift en
dc.title Maximal L p -regularity for the Laplacian on Lipschitz domains en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.contributor.institution Mathematics and Physics en
dc.description.status Peer reviewed en

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