Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.
Hodge Decomposition - a Method for Solving Boundary Value Problems
Rempel, S. and Schulze, B.-W. (1982). Index theory of elliptic boundary problems (Akademie-Verlag, Berlin). Schwarz, G. (1995). Hodge decomposition – A method for solving boundary value problems, Lecture Notes in Mathematics, Vol. 1607.
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds.
7 Visualization results of the head datasets with our opacity transfer functions (μ = 40,η = 0.05). ... show that our transfer function can effectively visualize the topological structure even if the number of critical points decreases.
[16] V.V. Kravchenko and M.V. Shapiro: Integral representations for spatial models of mathematical physics, Pitman Research Notes in Mathematics Series 351 Harlow: Longman, 1996. [17] M. Malonek; Power series representation for ...
A. H. Nasri ( 1997b ) , Interpolation of open curves by recursive subdivision surface , in The Mathematics of Surfaces VII ( T. Goodman and R. Martin ... J. Warren ( 19956 ) , Subdivision Methods for Geometric Design , Rice University .
[ 20 ] G. Schwarz : Hodge Decomposition A Method for Solving Boundary Value Problems . Lecture Notes in Mathematics 1607 , Springer - Verlag , Berlin ( 1995 ) [ 21 ] Z. Sun and G. Uhlmann : An inverse boundary value problem for ...
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Conference in Honor of James Ralston's 70th Birthday on Spectral Theory and Partial Differential Equations: June ... MR0355601 (50 #8075) G. Schwarz, Hodge decomposition—a method for solving boundary value problems, Lecture Volume 640, ...
To answer this fundamental problem in mathematics and physics, this book leads the reader to the frontier of inverse scattering theory for electromagnetism.The first three chapters, written comprehensively, can be used as a textbook for ...