Applications of Differential Calculus to Nonlinear Elliptic Boundary Value Problems with Discontinuous Coefficients
dc.contributor.author | Palagachev, Dian K. | |
dc.contributor.author | Recke, Lutz | |
dc.contributor.author | Softova, Lubomira G. | |
dc.date.accessioned | 2017-06-15T17:39:46Z | |
dc.date.available | 2017-06-15T17:39:46Z | |
dc.date.created | 2005-11-03 | |
dc.date.issued | 2005-11-03 | |
dc.identifier.issn | 0863-0976 | |
dc.identifier.uri | http://edoc.hu-berlin.de/18452/3245 | |
dc.description.abstract | We 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.iso | eng | |
dc.publisher | Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Implicit function theorems | eng |
dc.subject | Nonlinear boundary value problems for linear elliptic PDE | eng |
dc.subject | boundary value problems for nonlinear elliptic PDE | eng |
dc.subject | PDE with discontinuous coefficients or data | eng |
dc.subject | global Newton methods | eng |
dc.subject.ddc | 510 Mathematik | |
dc.title | Applications of Differential Calculus to Nonlinear Elliptic Boundary Value Problems with Discontinuous Coefficients | |
dc.type | book | |
dc.identifier.urn | urn:nbn:de:kobv:11-10052278 | |
dc.identifier.doi | http://dx.doi.org/10.18452/2593 | |
local.edoc.pages | 16 | |
local.edoc.type-name | Buch | |
local.edoc.container-type | series | |
local.edoc.container-type-name | Schriftenreihe | |
local.edoc.container-year | 2004 | |
dc.identifier.zdb | 2075199-0 | |
bua.series.name | Preprints aus dem Institut für Mathematik | |
bua.series.issuenumber | 2004,21 |