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2005-11-03Buch DOI: 10.18452/2593
Applications of Differential Calculus to Nonlinear Elliptic Boundary Value Problems with Discontinuous Coefficients
dc.contributor.authorPalagachev, Dian K.
dc.contributor.authorRecke, Lutz
dc.contributor.authorSoftova, Lubomira G.
dc.date.accessioned2017-06-15T17:39:46Z
dc.date.available2017-06-15T17:39:46Z
dc.date.created2005-11-03
dc.date.issued2005-11-03
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3245
dc.description.abstractWe deal with Dirichlet's problem for second order quasilinear non-divergence form elliptic equations with discontinuous coefficients. First we state suitable structure, growth, and regularity conditions ensuring solvability of the problem under consideration. Then we fix a solution $u_0$ such that the linearized in $u_0$ problem is non-degenerate, and we apply the Implicit Function Theorem: For all small perturbations of the coefficient functions there exists exactly one solution $u \approx u_0,$ and $u$ depends smoothly (in $W^{2,p}$ with $p$ larger than the space dimension) on the data. For that no structure and growth conditions are needed, and the perturbations of the coefficient functions can be general $L^\infty$-functions with respect to the space variable $x$. Moreover we show that the Newton Iteration Procedure can be applied to calculate a sequence of approximate (in $W^{2,p}$ again) solutions for $u_0.$eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectImplicit function theoremseng
dc.subjectNonlinear boundary value problems for linear elliptic PDEeng
dc.subjectboundary value problems for nonlinear elliptic PDEeng
dc.subjectPDE with discontinuous coefficients or dataeng
dc.subjectglobal Newton methodseng
dc.subject.ddc510 Mathematik
dc.titleApplications of Differential Calculus to Nonlinear Elliptic Boundary Value Problems with Discontinuous Coefficients
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10052278
dc.identifier.doihttp://dx.doi.org/10.18452/2593
local.edoc.pages16
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-year2004
dc.identifier.zdb2075199-0
bua.series.namePreprints aus dem Institut für Mathematik
bua.series.issuenumber2004,21

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