Sökning: "Björn Sjödin"

Visar resultat 1 - 5 av 11 avhandlingar innehållade orden Björn Sjödin.

1. 1. 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

3. 2. 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

4. 3. Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces

   Författare :Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Andrea Cianchi; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Newtonian space; Sobolev-type space; metric measure space; upper gradient; Sobolev capacity; Banach function lattice; quasi-normed space; rearrangement-invariant space; maximal operator; Lipschitz function; regularization; weak boundedness; density of Lipschitz functions; quasi-continuity; continuity; doubling measure; Poincaré inequality;

   Sammanfattning : This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. LÄS MER

5. 4. Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form

   Författare :Abubakar Mwasa; Jana Björn; Anders Björn; Tomas Sjödin; Sorina Barza; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : The thesis consists of three papers focussing on the study of nonlinear elliptic partial differential equations in a nonempty open subset Ω of the n-dimensional Euclidean space Rn. We study the existence and uniqueness of the solutions, as well as their behaviour near the boundary of Ω. LÄS MER

7. 5. 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