Linear and quasilinear parabolic equations in Sobolev space
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We consider linear parabolic equations of second order in a Sobolev space setting. We obtain existence and uniqueness results for such equations on a closed two-dimensional manifold, with minimal assumptions about the regularity of the coefficients of the elliptic operator. In particular, we derive a priori estimates relating the Sobolev regularity of the coefficients of the elliptic operator to that of the solution. The results obtained are used in conjunction with an iteration argument to...[Show more]
dc.contributor.author | Sharples, Jade | |
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dc.date.accessioned | 2015-12-13T22:43:49Z | |
dc.date.available | 2015-12-13T22:43:49Z | |
dc.identifier.issn | 0022-0396 | |
dc.identifier.uri | http://hdl.handle.net/1885/79374 | |
dc.description.abstract | We consider linear parabolic equations of second order in a Sobolev space setting. We obtain existence and uniqueness results for such equations on a closed two-dimensional manifold, with minimal assumptions about the regularity of the coefficients of the elliptic operator. In particular, we derive a priori estimates relating the Sobolev regularity of the coefficients of the elliptic operator to that of the solution. The results obtained are used in conjunction with an iteration argument to yield existence results for quasilinear parabolic equations. | |
dc.publisher | Academic Press | |
dc.source | Journal of Differential Equations | |
dc.subject | Keywords: A priori estimates; Parabolic equations; Sobolev space | |
dc.title | Linear and quasilinear parabolic equations in Sobolev space | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
local.identifier.citationvolume | 202 | |
dc.date.issued | 2004 | |
local.identifier.absfor | 010110 - Partial Differential Equations | |
local.identifier.ariespublication | MigratedxPub7829 | |
local.type.status | Published Version | |
local.contributor.affiliation | Sharples, Jade, College of Medicine, Biology and Environment, ANU | |
local.bibliographicCitation.issue | 1 | |
local.bibliographicCitation.startpage | 111 | |
local.bibliographicCitation.lastpage | 142 | |
local.identifier.doi | 10.1016/j.jde.2004.03.020 | |
dc.date.updated | 2015-12-11T10:14:25Z | |
local.identifier.scopusID | 2-s2.0-3543105561 | |
Collections | ANU Research Publications |
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