Search for dissertations about: "metric measure space"

Showing result 1 - 5 of 11 swedish dissertations containing the words metric measure space.

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

    Author : Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Andrea Cianchi; Linköpings universitet; []
    Keywords : 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;

    Abstract : 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. READ MORE

  4. 2. Measures of Freedom of Choice

    Author : Karin Enflo; Erik Carlson; Thomas Anderberg; Martin van Hees; Uppsala universitet; []
    Keywords : HUMANIORA; HUMANITIES; Freedom of Choice; Measure; Choice Set; Diversity; Cardinality; Evenness; Decision Theory; Metric Space; Practical Philosophy; Praktisk filosofi;

    Abstract : This thesis studies the problem of measuring freedom of choice. It analyzes the concept of freedom of choice, discusses conditions that a measure should satisfy, and introduces a new class of measures that uniquely satisfy ten proposed conditions. READ MORE

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

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

    Abstract : 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. READ MORE

  6. 4. The Double Obstacle Problem on Metric Spaces

    Author : Zohra Farnana; Jan Björn; Anders Björn; Juha Kinnunen; Linköpings universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; metric space; nonlinear; obstacle problem; p-harmonic; potential theory; regularity; stability; MATHEMATICS; MATEMATIK;

    Abstract : During the last decade, potential theory and p-harmonic functions have been developed in the setting of doubling metric measure spaces supporting a p-Poincar´e inequality. This theory unifies, and has applications in several areas of analysis, such as weighted Sobolev spaces, calculus on Riemannian manifolds and Carnot groups, subelliptic differential operators and potential theory on graphs. READ MORE

  7. 5. Stable iterated function systems

    Author : Erland Gadde; Hans Wallin; Umeå universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Hausdorff metric; iterated function system IFS ; attractor; invariant set; address; Hutchinson’s metric; we a k* -topology; IFS with probabilities; invariant measure; the Random Iteration Algorithm;

    Abstract : The purpose of this thesis is to generalize the growing theory of iterated function systems (IFSs). Earlier, hyperbolic IFSs with finitely many functions have been studied extensively. Also, hyperbolic IFSs with infinitely many functions have been studied. In this thesis, more general IFSs are studied. READ MORE