Björn, Jana
Overview
Works:  56 works in 100 publications in 1 language and 276 library holdings 

Genres:  Academic theses 
Roles:  Author, Other, Contributor, the 
Publication Timeline
.
Most widely held works by
Jana Björn
Nonlinear potential theory on metric spaces by
Anders Björn(
Book
)
11 editions published in 2011 in English and held by 160 WorldCat member libraries worldwide
The pLaplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory and image processing. Its solutions, called pharmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs and Heisenberg groups. Nonlinear potential theory of pharmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for an interested reader and as a reference text for an active researcher. The presentation is rather selfcontained, but the reader is assumed to know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, socalled Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study pharmonic functions on metric spaces and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references and an extensive index is provided at the end of the book
11 editions published in 2011 in English and held by 160 WorldCat member libraries worldwide
The pLaplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory and image processing. Its solutions, called pharmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs and Heisenberg groups. Nonlinear potential theory of pharmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for an interested reader and as a reference text for an active researcher. The presentation is rather selfcontained, but the reader is assumed to know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, socalled Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study pharmonic functions on metric spaces and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references and an extensive index is provided at the end of the book
Nonlinear potential theory on metric spaces by
Anders Björn(
)
1 edition published in 2011 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 16 WorldCat member libraries worldwide
The Perron method for pharmonic functions by
Anders Björn(
Book
)
4 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
4 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
Admissible measures in one dimension by
Jana Björn(
Book
)
3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
Boundary regularity for pharmonic functions and solutions of the obstacle problem on metric spaces by Anders Björn(
Book
)
3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
A problem of Baernstein on the equality of the pharmonic measure of a set and its closure by Anders Björn(
Book
)
4 editions published between 2003 and 2006 in English and held by 4 WorldCat member libraries worldwide
A. Baernstein II ( Comparison of pharmonic measures of subsets of the unit circle , St. Petersburg Math. J. 9 (1998), 543551, p. 548), posed the following question: If G is a union of m open arcs on the boundary of the unit disc D, then is w a,p (G)=w a,p (G), where w a,p denotes the pharmonic measure? (Strictly speaking he stated this question for the case m=2.) For p=2 the positive answer to this question is well known. Recall that for p≠2 the pharmonic measure, being a nonlinear analogue of the harmonic measure, is not a measure in the usual sense. The purpose of this note is to answer a more general version of Baernstein's question in the affirmative when 1G is the restriction to ∂D of a Sobolev function from W 1,p (C). For p≥2 it is no longer true that X G belongs to the trace class. Nevertheless, we are able to show equality for the case m=1 of one arc for all 1, using a very elementary argument. A similar argument is used to obtain a result for starshaped domains. Finally we show that in a certain sense the equality holds for almost all relatively open sets
4 editions published between 2003 and 2006 in English and held by 4 WorldCat member libraries worldwide
A. Baernstein II ( Comparison of pharmonic measures of subsets of the unit circle , St. Petersburg Math. J. 9 (1998), 543551, p. 548), posed the following question: If G is a union of m open arcs on the boundary of the unit disc D, then is w a,p (G)=w a,p (G), where w a,p denotes the pharmonic measure? (Strictly speaking he stated this question for the case m=2.) For p=2 the positive answer to this question is well known. Recall that for p≠2 the pharmonic measure, being a nonlinear analogue of the harmonic measure, is not a measure in the usual sense. The purpose of this note is to answer a more general version of Baernstein's question in the affirmative when 1G is the restriction to ∂D of a Sobolev function from W 1,p (C). For p≥2 it is no longer true that X G belongs to the trace class. Nevertheless, we are able to show equality for the case m=1 of one arc for all 1, using a very elementary argument. A similar argument is used to obtain a result for starshaped domains. Finally we show that in a certain sense the equality holds for almost all relatively open sets
Boundary continuity for quasiminimizers on metric spaces by
Jana Björn(
Book
)
4 editions published in 2000 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 2000 in English and held by 4 WorldCat member libraries worldwide
Boundedness and differentiability a.e. for systems of elliptic equations and variational inequalities : Lpdifferentials for
weighted Sobolev spaces by
Jana Björn(
Book
)
4 editions published in 1999 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1999 in English and held by 4 WorldCat member libraries worldwide
Approximation by regular sets in metric spaces by
Jana Björn(
Book
)
3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
The Dirichlet problem for pharmonic functions on metric measure spaces by
Anders Björn(
Book
)
4 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
Interior regularity and boundary behaviour of solutions to second order elliptic equations by
Jana Björn(
Book
)
4 editions published in 1996 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1996 in English and held by 4 WorldCat member libraries worldwide
Poincaré inequalities for powers and products of admissible weights by
Jana Björn(
Book
)
3 editions published in 1999 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 3 WorldCat member libraries worldwide
Sobolev extensions of Hölder continous and characteristic functions on metric spaces by
Anders Björn(
Book
)
2 editions published in 2005 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2005 in English and held by 3 WorldCat member libraries worldwide
Orlicz capacities and Hausdorff measures on metric spaces by
Jana Björn(
Book
)
2 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide
Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form by
Jana Björn(
Book
)
3 editions published in 1997 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1997 in English and held by 3 WorldCat member libraries worldwide
Boundary Regularity for the Porous Medium Equation by Anders Björn(
)
2 editions published in 2018 in English and held by 3 WorldCat member libraries worldwide
We study the boundary regularity of solutions to the porous medium equation in the degenerate range . In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for generalnot necessarily cylindricaldomains in . One of our fundamental tools is a new strict comparison principle between sub and superparabolic functions, which makes it essential for us to study both nonstrict and strict Perron solutions to be able to develop a fruitful boundary regularity theory. Several other comparison principles and pasting lemmas are also obtained. In the process we obtain a rather complete picture of the relation between sub/superparabolic functions and weak sub/supersolutions
2 editions published in 2018 in English and held by 3 WorldCat member libraries worldwide
We study the boundary regularity of solutions to the porous medium equation in the degenerate range . In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for generalnot necessarily cylindricaldomains in . One of our fundamental tools is a new strict comparison principle between sub and superparabolic functions, which makes it essential for us to study both nonstrict and strict Perron solutions to be able to develop a fruitful boundary regularity theory. Several other comparison principles and pasting lemmas are also obtained. In the process we obtain a rather complete picture of the relation between sub/superparabolic functions and weak sub/supersolutions
Quasicontinuity of NewtonSobolev functions and density of Lipschitz functions on metric spaces by
Anders Björn(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
The annular decay property and capacity estimates for thin annuli by Anders Björn(
)
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces by Anders Björn(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
The Mazurkiewicz Distance and Sets that are Finitely Connected at the Boundary by Anders Björn(
)
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Björn, Anders 1966 Author
 Shanmugalingam, Nageswari Contributor
 Björn, Anders Author
 Universitetet i Linköping Matematiska institutionen Publisher
 SpringerLink (Online service) Other
 Linköpings universitet Tekniska högskolan Publisher
 Lehrbäck, Juha Other
 Maz'ya, Vladimir
 Gianazza, Ugo Other Contributor
 Universitetet i Linkzoping Department of Mathematics
Associated Subjects