scholarly journals Regularity theory for the Isaacs equation through approximation methods

2019 ◽  
Vol 36 (1) ◽  
pp. 53-74 ◽  
Author(s):  
Edgard A. Pimentel
Keyword(s):  
Regularity Theory ◽  
Approximation Methods ◽  
Isaacs Equation

A study of direct vs. approximation methods in structural optimization

1995 ◽  
Vol 10 (1) ◽  
pp. 64-66 ◽  
Author(s):  
Y. -S. Park ◽  
S. -H. Lee ◽  
G. -J. Park
Keyword(s):  
Structural Optimization ◽  
Approximation Methods

scholarly journals Volume decay and concentration of high-dimensional Euclidean balls – a PDE and variational perspective

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Siran Li
Keyword(s):  
Banach Space ◽  
Discrete Geometry ◽  
Thin Shell ◽  
Euclidean Geometry ◽  
Convex Geometry ◽  
Regularity Theory ◽  
Elliptic Partial Differential Equations ◽  
High Dimensional ◽  
Space Theory ◽  
Elementary Calculus

AbstractIt is a well-known fact – which can be shown by elementary calculus – that the volume of the unit ball in \mathbb{R}^{n} decays to zero and simultaneously gets concentrated on the thin shell near the boundary sphere as n\nearrow\infty. Many rigorous proofs and heuristic arguments are provided for this fact from different viewpoints, including Euclidean geometry, convex geometry, Banach space theory, combinatorics, probability, discrete geometry, etc. In this note, we give yet another two proofs via the regularity theory of elliptic partial differential equations and calculus of variations.

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