Sökning: "Tomas Sjödin"

Visar resultat 1 - 5 av 7 avhandlingar innehållade orden Tomas Sjödin.

1. 1. Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure

   Författare :Tomas Sjödin; Björn Gustafsson; Stephen Gardiner; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; Quadrature Domain; Balayage; Harmonic measure; Martin boundary; Matematisk analys; Mathematical analysis; Analys;

   Sammanfattning : In this thesis, which consists of five papers (A,B,C,D,E), we are interested in questions related to quadrature domains. Among the problems studied are the possibility of changing the type of measure in a quadrature identity (from complex to real and from real signed to positive), properties of partial balayage, which in a sense can be used to generate quadrature domains, and mother bodies which are closely related to inversion of partial balayage. LÄS MER

3. 2. Capacities, Poincaré inequalities and gluing metric spaces

   Författare :Andreas Christensen; Anders Björn; Jana Björn; Tomas Sjödin; Tapio Rajala; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : This thesis consists of an introduction, and one research paper with results related to potential theory both in the classical Euclidean setting, as well as in quite general metric spaces.The introduction contains a theoretical and historical background of some basic concepts, and their more modern generalisations to metric spaces developed in the last 30 years. LÄS MER

4. 3. Two Problems in non-linear PDE’s with Phase Transitions

   Författare :Karl Jonsson; Henrik Shahgholian; Tomas Sjödin; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Conductivity jump; Free boundary problem; Quasilinear elliptic equation; Mathematical techniques; Nonlinear analysis; Free boundary; Free-boundary problems; Quasi-linear elliptic; Quasilinear elliptic equations; Hele-Shaw flow; non-local; implicit function theorem; Heterogeneous Multi Scale; HMM; Finite Element; FEM; FE; Mathematics; Matematik;

   Sammanfattning : This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. LÄS MER

5. 4. Small-amplitude steady water waves with vorticity

   Författare :Evgeniy Lokharu; Vladimir Kozlov; Johan Thim; Tomas Sjödin; Mark Groves; Linköpings universitet; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY;

   Sammanfattning : The problem of describing two-dimensional traveling water waves is considered. The water region is of finite depth and the interface between the region and the air is given by the graph of a function. We assume the flow to be incompressible and neglect the effects of surface tension. LÄS MER

7. 5. Newtonian Spaces Based on Quasi-Banach Function Lattices

   Författare :Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Pekka Koskela; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Newtonian space; upper gradient; weak upper gradient; Banach function lattice; quasi-normed space; metric measure space;

   Sammanfattning : The traditional first-order analysis in Euclidean spaces relies on the Sobolev spaces W1,p(Ω), where Ω ⊂ Rn is open and p ∈ [1, ∞].The Sobolev norm is then defined as the sum of Lp norms of a function and its distributional gradient.We generalize the notion of Sobolev spaces in two different ways. LÄS MER