Sökning: "doubling measure"

Visar resultat 1 - 5 av 15 avhandlingar innehållade orden doubling measure.

  1. 1. 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

  3. 2. Boundary Estimates for Solutions to Parabolic Equations

    Författare :Olow Sande; Kaj Nyström; Maciej Klimek; Juha Kinnunen; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Uniformly parabolic equations; non-linear parabolic equations; linear growth; degenerate parabolic equations; fractional heat equations; complex coefficients; Lipschitz domain; NTA domain; boundary behaviour; boundary Harnack; parabolic measure; Riesz measure; Dirichlet to Neumann map; single layer potentials.; Mathematics; Matematik;

    Sammanfattning : This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation.Paper I concerns the solutions to non-linear parabolic equations with linear growth. LÄS MER

  4. 3. Studies of the Boundary Behaviour of Functions Related to Partial Differential Equations and Several Complex Variables

    Författare :Håkan Persson; Kaj Nyström; Maciej Klimek; Evgeny Poletsky; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; uniformly parabolic equations; non-linear parabolic equations; linear growth; Lipschitz domain; NTA-domain; Riesz measure; boundary behavior; boundary Harnack; degenerate parabolic; parabolic measure; plurisubharmonic functions; continuous boundary; hyperconvexity; bounded exhaustion function; Hölder for all exponents; log-lipschitz; boundary regularity; approximation; Mergelyan type approximation; plurisubharmonic functions on compacts; Jensen measures; monotone convergence; plurisubharmonic extension; plurisubharmonic boundary values; Mathematics; Matematik;

    Sammanfattning : This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables.Paper I concerns solutions to non-linear parabolic equations of linear growth. LÄS MER

  5. 4. On parabolic equations of Kolmogorov-Fokker-Planck type

    Författare :Malte Litsgård; Kaj Nyström; Ugo Gianazza; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Kolmogorov equation; degenerate parabolic; ultraparabolic; Lipschitz domain; Dirichlet problem; boundary behaviour; parabolic measure.; Mathematics; Matematik;

    Sammanfattning : In this thesis solutions to Kolmogorov-Fokker-Planck type equations are studied. It consists of a comprehensive summary and four scientific articles.In the first article a potential theory for certain strongly degenerate parabolic operators in unbounded domains of Lipschitz type is developed. LÄS MER

  7. 5. 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