Search for dissertations about: "metric measure space"
Showing result 1 - 5 of 11 swedish dissertations containing the words metric measure space.
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1. Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces
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
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2. Measures of Freedom of Choice
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
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3. Newtonian Spaces Based on Quasi-Banach Function Lattices
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
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4. The Double Obstacle Problem on Metric Spaces
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
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5. Stable iterated function systems
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