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Applications of Fou...
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Aleksanyan, HaykKTH,Matematik (Avd.),The University of Edinburgh
(författare)
Applications of Fourier Analysis in Homogenization of the Dirichlet Problem : L-p Estimates
- Artikel/kapitelEngelska2015
Förlag, utgivningsår, omfång ...
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2014-08-08
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Springer,2015
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printrdacarrier
Nummerbeteckningar
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LIBRIS-ID:oai:DiVA.org:kth-159614
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https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-159614URI
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https://doi.org/10.1007/s00205-014-0774-5DOI
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Språk:engelska
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Sammanfattning på:engelska
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Ämneskategori:art swepub-publicationtype
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QC 20150209
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Let u(epsilon) be a solution to the system div(A(epsilon)(x)del u(epsilon)(x)) = 0 in D, u(epsilon)(x) = g(x, x/epsilon) on partial derivative D, where D subset of R-d (d >= 2), is a smooth uniformly convex domain, and g is 1-periodic in its second variable, and both A(epsilon) and g are sufficiently smooth. Our results in this paper are twofold. First we prove L-p convergence results for solutions of the above system and for the non-oscillating operator A(epsilon)(x) = A(x), with the following convergence rate for all 1 <= p < infinity parallel to u(epsilon) - u(0)parallel to (LP(D)) <= C-P {epsilon(1/2p), d = 2, (epsilon vertical bar ln epsilon vertical bar)(1/p), d = 3, epsilon(1/p), d >= 4, which we prove is (generically) sharp for d >= 4. Here u(0) is the solution to the averaging problem. Second, combining our method with the recent results due to Kenig, Lin and Shen (Commun Pure Appl Math 67(8): 1219-1262, 2014), we prove (for certain class of operators and when d >= 3) ||u(epsilon) - u(0)||(Lp(D)) <= C-p[epsilon(ln(1/epsilon))(2)](1/p) for both the oscillating operator and boundary data. For this case, we take A(epsilon) = A(x/epsilon), where A is 1-periodic as well. Some further applications of the method to the homogenization of the Neumann problem with oscillating boundary data are also considered.
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Biuppslag (personer, institutioner, konferenser, titlar ...)
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Shahgholian, HenrikKTH,Matematik (Inst.)(Swepub:kth)u15h3xoo
(författare)
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Sjölin, PerKTH,Matematik (Inst.)(Swepub:kth)u1lbeqv9
(författare)
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KTHMatematik (Avd.)
(creator_code:org_t)
Sammanhörande titlar
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Ingår i:Archive for Rational Mechanics and Analysis: Springer215:1, s. 65-870003-95271432-0673
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