Universität zu Köln

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

Preview

PDF main.pdf - Accepted Version Download (2MB)

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:	Creators Email ORCID ORCID Put Code Beygmohammadi, Maryam mbeygmoh@math.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-64432
Date:	10 November 2015
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Partial Differential Equations, Laplace equation, Hopf's boundary point lemma, singular boundary point, not-smooth domains, conical point English
Date of oral exam:	19 October 2015
Referee:	Name Academic Title Sweers, Guido Prof. Dr. Kawohl, Bernd Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/6443