Universität zu Köln

Hopf's Type Estimates near Singular Boundary Points

Beygmohammadi, Maryam (2015) Hopf's Type Estimates near Singular Boundary Points. PhD thesis, Universität zu Köln.

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    Abstract

    Subject of this thesis is the behaviour of the solution of the Laplace-Poisson equation under zero Dirichlet boundary condition near non-regular boundary points. The first part gives an example of a domain where Hopf's Boundary Point Lemma holds true pointwise but not uniformly, therefore the solution operator is not strongly positive. A second result addresses a sharp replacement of Hopf's estimate near the boundary whenever such boundary has a conical point. As a consequence one is able to prove an optimal anti-maximum type result for domains with conical shapes. The last part is concerned with the behaviour of the solution at points where an interface reaches the boundary. At the interface the Poisson equation is not satisfied but instead a jump condition for the normal derivatives appears.

    Item Type: Thesis (PhD thesis)
    Creators:
    CreatorsEmail
    Beygmohammadi, Maryammbeygmoh@math.uni-koeln.de
    URN: urn:nbn:de:hbz:38-64432
    Subjects: Mathematics
    Uncontrolled Keywords:
    KeywordsLanguage
    Partial Differential Equations, Laplace equation, Hopf's boundary point lemma, singular boundary point, not-smooth domains, conical pointEnglish
    Faculty: Mathematisch-Naturwissenschaftliche Fakultät
    Divisions: Mathematisch-Naturwissenschaftliche Fakultät > Mathematisches Institut
    Language: English
    Date: 10 November 2015
    Date Type: Publication
    Date of oral exam: 19 October 2015
    Full Text Status: Public
    Date Deposited: 10 Dec 2015 14:57:55
    Referee
    NameAcademic Title
    Sweers, GuidoProf. Dr.
    Kawohl, BerndProf. Dr.
    URI: http://kups.ub.uni-koeln.de/id/eprint/6443

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