Search for dissertations about: "Sobolev-type space"

Showing result 1 - 5 of 7 swedish dissertations containing the words Sobolev-type 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. 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

  5. 3. Embedding theorems for spaces with multiweighted derivatives

    Author : Zamira Abdikalikova; Luleå tekniska universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Matematik; Mathematics;

    Abstract : This Licentiate Thesis consists of four chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. READ MORE

  6. 4. Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives

    Author : Zamira Abdikalikova; Victor Burenkov; Luleå tekniska universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

    Abstract : This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions. READ MORE

  7. 5. A new development of Nikol'skii - Lizorkin and Hardy type inequalities with applications

    Author : Aigerim Kalybay; Luleå tekniska universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Matematik; Mathematics;

    Abstract : This thesis consists of an introduction and five papers, which all deal with a new Sobolev type function space called the space with multiweighted derivatives. As basis for this space serves some differential operators containing weight functions. READ MORE