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http://hdl.handle.net/10773/23634
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DC Field | Value | Language |
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dc.contributor.author | Leonetti, Francesco | pt |
dc.contributor.author | Rocha, Eugenio | pt |
dc.contributor.author | Staicu, Vasile | pt |
dc.date.accessioned | 2018-06-22T11:34:00Z | - |
dc.date.issued | 2018-09-15 | - |
dc.identifier.issn | 0022-247X | pt |
dc.identifier.uri | http://hdl.handle.net/10773/23634 | - |
dc.description.abstract | In a bounded open subset Ω ⊂ Rn, we study Dirichlet problems with elliptic systems, involving a finite Radon measure μ on Rn with values into RN , defined by { −div A(x, u(x), Du(x)) = μ in Ω, u = 0 on ∂Ω, where Aα i (x, y, ξ) = N∑ β=1 n∑ j=1 aα,β i,j (x, y) ξβ j with α ∈ {1, . . . , N } the equation index. We prove the existence of a (distributional) solution u : Ω → RN , obtained as the limit of approximations, by assuming: (i) that coefficients aα,β i,j are bounded Carathéodory functions; (ii) ellipticity of the diagonal coefficients aα,α i,j ; and (iii) smallness of the quadratic form associated to the off-diagonal coefficients aα,β i,j (i.e. α = β) verifying a r-staircase support condition with r > 0. Such a smallness condition is satisfied, for instance, in each one of these cases: (a) aα,β i,j = −aβ,α j,i (skew-symmetry); (b) |aα,β i,j | is small; (c) aα,β i,j may be decomposed into two parts, the first enjoying skew-symmetry and the second being small in absolute value. We give an example that satisfies our hypotheses but does not satisfy assumptions introduced in previous works. A Brezis’s type nonexistence result is also given for general (smooth) elliptic-hyperbolic systems. | pt |
dc.language.iso | eng | pt |
dc.publisher | Elsevier | pt |
dc.relation | info:eu-repo/grantAgreement/FCT/5876/147206/PT | pt |
dc.rights | openAccess | por |
dc.subject | Elliptic | pt |
dc.subject | System | pt |
dc.subject | Existence | pt |
dc.subject | Measure | pt |
dc.subject | Solution | pt |
dc.title | Smallness and cancellation in some elliptic systems with measure data | pt |
dc.type | article | pt |
dc.peerreviewed | yes | pt |
ua.distribution | international | pt |
degois.publication.firstPage | 885 | pt |
degois.publication.issue | 2 | pt |
degois.publication.lastPage | 902 | pt |
degois.publication.title | Journal of Mathematical Analysis and Applications | pt |
degois.publication.volume | 465 | pt |
dc.date.embargo | 10000-01-01 | - |
dc.identifier.doi | 10.1016/j.jmaa.2018.05.047 | pt |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Size | Format | |
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Smallness and cancellation in some elliptic systems with measure data.pdf | 416.14 kB | Adobe PDF | View/Open |
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