Existence, multiplicity and behaviour of solutions of some elliptic partial differential equations of higher order

Autor :Edoardo Sassone
Herkunft :OvGU Magdeburg, Fakultät für Mathematik
Datum :20.01.2009
Dokumente :
Dataobject from HALCoRe_document_00008258
Typ :Dissertation
Format :Text
Kurzfassung :We are interested in questions related with existence, multiplicity, positivity and behaviour of solutions of elliptic boundary value problems of second and higher order. In general problems $(-\Delta)^m u=f$ in $\Omega\subset\mathbb{R}^2$, $\partial^j / (\partial\nu)^j u=0$ on $\partial\Omega$, where $m>1$, $0\le j\le m-1$ do not satisfy a maximum principle or the positivity preserving property. We will show that for domains near to a circle positivity preserving property is satisfied. Then we will give some results of existence and multiplicity of solutions of the Steklov problem of second and fourth order. Finally we will characterize singular radial solutions of $\Delta^2u=\lambda e^u$ in the unit disk, with boundary conditions $u=\partial u/ \partial\nu=0$. We will show that its radial singular solutions are weakly singular, it means $\lim_{r\rightarrow 0} ru'(r)\in\mathbb{R}$ exists.
Schlagwörter :PDE
Rechte :Dieser Text ist urheberrechtlich geschützt
Größe :69 S.
Erstellt am :27.07.2010 - 11:45:54
Letzte Änderung :27.07.2010 - 11:46:25
MyCoRe ID :HALCoRe_document_00008258
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