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Analyticity of laye...
Analyticity of layer potentials and L-2 solvability of boundary value problems for divergence form elliptic equations with complex L-infinity coefficients
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- Alfonseca, M Angeles (författare)
- N Dakota State University
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- Auscher, Pascal (författare)
- University Paris 11
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- Axelsson Rosén, Andreas (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska högskolan
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- Hofmann, Steve (författare)
- University of Missouri
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- Kim, Seick (författare)
- Yonsei University
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(creator_code:org_t)
- Elsevier Science B.V. Amsterdam, 2011
- 2011
- Engelska.
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Ingår i: Advances in Mathematics. - : Elsevier Science B.V. Amsterdam. - 0001-8708 .- 1090-2082. ; 226:5, s. 4533-4606
- Relaterad länk:
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https://doi.org/10.1...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We consider divergence form elliptic operators of the form L = -div A (x)del, defined in Rn+1 = {(x, t) is an element of R-n x R}, n andgt;= 2, where the L-infinity coefficient matrix A is (n + 1) x (n + 1), uniformly elliptic, complex and t-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on L-2 (R-n) = L-2(partial derivative R-+(n+1)) is stable under complex, L-infinity perturbations of the coefficient matrix. Using a variant of the Tb Theorem, we also prove that the layer potentials are bounded and invertible on L-2(R-n) whenever A (x) is real and symmetric (and thus, by our stability result, also when A is complex, parallel to A - A(0)parallel to(infinity) is small enough and A(0) is real, symmetric, L-infinity and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with L-2 (resp. (L) over dot(1)(2)) data, for small complex perturbations of a real symmetric matrix. Previously, L-2 solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients A (j,n+1)= 0 = A(n+1,j), 1 andlt;= j andlt;= n, which corresponds to the Kato square root problem.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Singular integrals
- Square functions
- Layer potentials
- Divergence form elliptic equations
- Local Tb theorem
- MATHEMATICS
- MATEMATIK
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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