Notes on the Infinity Laplace Equation

Peter Lindqvist (Autor)

Buch | Softcover

IX, 68 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-31531-7 (ISBN)

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This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity-Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

Peter LindqvistProfessor of Mathematics Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim, Norway Research interests: Analysis, in particular partial differential equations and "nonlinear potential theory"

1 Introduction.- 2 Preliminaries.- 3 Variational Solutions.- 4 Viscosity Solutions.- 5 An Asymptotic Mean Value Formula.- 6 Comparison with Cones.- 7 From the Theory of Viscosity Solutions.- 8 Uniqueness of Viscosity Solutions.- 9 Tug-of-War.- 10 The Equation 1v = F.

"This book is an excellent introduction to the infinity Laplacian- it is informative and has up-to-date references." (Fernando Charro, Mathematical Reviews, April 2017)

“This book is an excellent introduction to the infinity Laplacian— it is informative and has up-to-date references.” (Fernando Charro, Mathematical Reviews, April 2017)

Erscheinungsdatum	08.10.2016
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	IX, 68 p. 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Grafik / Design ► Digitale Bildverarbeitung
	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	computational science and engineering • Degenerate elliptic equations • Fully non-linear equations • image processing and computer vision • Lipschitz extensions • mathematics and statistics • Ordinary differential equations • Partial differential equations • PDE • The infinity laplace operator • Viscosity Solutions
ISBN-10	3-319-31531-5 / 3319315315
ISBN-13	978-3-319-31531-7 / 9783319315317
Zustand	Neuware