WorldCat Identities

Martio, O. (Olli)

Overview
Works: 198 works in 279 publications in 1 language and 1,665 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Other, Honoree, Contributor
Publication Timeline
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Most widely held works by O Martio
Moduli in modern mapping theory by O Martio( )

18 editions published between 2008 and 2009 in English and Undetermined and held by 502 WorldCat member libraries worldwide

The purpose of this book is to present a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations.--
Nonlinear potential theory of degenerate elliptic equations by Juha Heinonen( Book )

24 editions published between 1993 and 2018 in English and Undetermined and held by 431 WorldCat member libraries worldwide

A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions.Starting with the theory of weighted Sobolev spaces, this treatment advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The text concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes
Infinitesimal geometry of quasiconformal and bi-Lipschitz mappings in the plane by Bogdan Bojarski( Book )

3 editions published in 2013 in English and held by 102 WorldCat member libraries worldwide

"This book is intended for researchers interested in new aspects of local behavior of plane mappings and their applications. The presentation is self-contained, but the reader is assumed to know basic complex and real analysis. The study of the local and boundary behavior of quasiconformal and bi-Lipschitz mappings in the plane forms the core of the book. The concept of the infinitesimal space is used to investigate the behavior of a mapping at points without differentiability. This concept, based on compactness properties, is applied to regularity problems of quasiconformal mappings and quasiconformal curves, boundary behavior, weak and asymptotic conformality, local winding properties, variation of quasiconformal mappings, and criteria of univalence. Quasiconformal and bi-Lipschitz mappings are instrumental for understanding elasticity, control theory and tomography and the book also offers a new look at the classical areas such as the boundary regularity of a conformal map. Complicated local behavior is illustrated by many examples. The text offers a detailed development of the background for graduate students and researchers. Starting with the classical methods to study quasiconformal mappings, this treatment advances to the concept of the infinitesimal space and then relates it to other regularity properties of mappings in Part II. The new unexpected connections between quasiconformal and bi-Lipschitz mappings are treated in Part III. There is an extensive bibliography"--Page 4 of cover
XVI Rolf Nevanlinna Colloquium : proceedings of the international conference held in Joensuu, Finland, August 1-5, 1995 by Rolf Nevanlinna-Kolloquium( Book )

3 editions published in 1996 in English and held by 47 WorldCat member libraries worldwide

Topological and metric properties of quasiregular mappings by O Martio( Book )

3 editions published in 1971 in English and held by 38 WorldCat member libraries worldwide

Proceedings of the Second Finnish-Polish Summer School in Complex Analysis at Jyväskylä by Finnish-Polish Summer School in Complex Analysis( Book )

1 edition published in 1984 in English and held by 28 WorldCat member libraries worldwide

Proceedings of the Summer School in Potential Theory at Jyväskylä by Summer School in potential theory( Book )

5 editions published in 1987 in English and held by 26 WorldCat member libraries worldwide

On harmonic quasiconformal mappings by O Martio( Book )

1 edition published in 1968 in English and held by 21 WorldCat member libraries worldwide

A capacity inequality for quasiregular mappings by O Martio( Book )

1 edition published in 1970 in English and held by 21 WorldCat member libraries worldwide

Boundary behavior of quasiregular mappings by O Martio( Book )

2 editions published in 1972 in English and held by 20 WorldCat member libraries worldwide

Measure properties of the branch set and its image of quasiregular mappings by O Martio( Book )

2 editions published in 1973 in English and held by 20 WorldCat member libraries worldwide

On variational integrals in "the borderline case" by O Martio( Book )

2 editions published in 1973 in English and held by 19 WorldCat member libraries worldwide

Definitions for quasiregular mappings by O Martio( Book )

3 editions published between 1969 and 1972 in English and held by 18 WorldCat member libraries worldwide

Distortion and singularities of quasiregular mappings by O Martio( Book )

1 edition published in 1970 in English and held by 15 WorldCat member libraries worldwide

Boundary values and injectiveness of the solutions of Beltrami equations by O Martio( Book )

1 edition published in 1967 in English and held by 15 WorldCat member libraries worldwide

A capacity inequality for quasiregular mappings by O Martio( Book )

1 edition published in 1970 in English and held by 15 WorldCat member libraries worldwide

Definitions for quasiregular mappings by O Martio( Book )

1 edition published in 1969 in English and held by 14 WorldCat member libraries worldwide

Boundary behavior of quasiregular mappings by O Martio( Book )

1 edition published in 1972 in English and held by 14 WorldCat member libraries worldwide

On harmonic quasiconformal mappings by O Martio( Book )

1 edition published in 1968 in English and held by 13 WorldCat member libraries worldwide

Papers on analysis : a volume dedicated to Olli Martio on the occasion of his 60th birthday by Juha Heinonen( Book )

4 editions published in 2001 in English and held by 12 WorldCat member libraries worldwide

 
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Nonlinear potential theory of degenerate elliptic equations
Covers
Nonlinear potential theory of degenerate elliptic equations
Alternative Names
Martio, O.

Martio, Olli

Olli Martio Finnish mathematician

Olli Martio suomalainen matemaatikko

Languages
English (76)