UID:
almahu_9949697896302882
Format:
1 online resource (259 p.)
ISBN:
1-281-79035-4
,
9786611790356
,
0-08-087202-6
Series Statement:
North-Holland mathematics studies ; 91
Content:
This book gives a unified presentation of different mathematical tools used to solve classical problems like Plateau's problem, Bernstein's problem, Dirichlet's problem for the Minimal Surface Equation and the Capillary problem.The fundamental idea is a quite elementary geometrical definition of codimension one surfaces. The isoperimetric property of the Euclidean balls, together with the modern theory of partial differential equations are used to solve the 19th Hilbert problem. Also included is a modern mathematical treatment of capillary problems.
Note:
Description based upon print version of record.
,
Front Cover; Minimal Surfaces of Codimension One; Copyright Page; Contents; Preface; Introduction; CHAPTER ONE. DIFFERENTIAL PROPERTIES OF SURFACES; 1.1. Analytic representation of surfaces; 1.2. Surfaces of constant mean curvature; 1.3. Surface area; 1.4. An isoperimetric inequality; 1.5. Minimal cones; 1.6. Slope of minimal graphs; 1.7. Bernstein theorem for five dimensional surfaces; CHAPTER TWO. SETS OF FINITE PERIMETER AND MINIMAL BOUNDARIES; 2.1. Sets of finite perimeter; 2.2 . The isoperimetric inequality; 2.3. Reduced boundary; 2.4. Minimal boundaries
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2.5. Smoothness of minimal boundaries2.6. Singular points of minimal surfaces; 2.7. simons cone; 2.8. Bernstein problem; CHAPTER THREE. THE DIRICHLET PROBLEM FOR THE MINIMAL SURFACE EQUATION; 3.1. The Hilbert - Haar existence theory; 3.2. Dirichlet principle; 3.3. Smoothness of Hilbert - Haar solutions, the 19th Hilbert problem; 3.4. The Dirichlet problem for the minimal surface equation . Case of strictly convex domains; 3.5. The Dirichlet problem for the minimal surface equation. General case; 3.6. Interior regularity; 3.7. Boundary behavior of variational solutions
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3.8. The capillary problemCHAPTER FOUR. UNBOUNDED SOLUTIONS; 4.1. Generalized solutions . Definition; 4.2. Compactness of generalized solutions; 4.3. Dirichlet problem with infinite data; 4.4. Dirichlet problem on unbounded sets; 4.5. Removable singularities; Appendix; References; Analytic index; List of symbols
,
English
Additional Edition:
ISBN 0-444-86873-9
Language:
English
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