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Comparison principles in capillarity
1988Introductory remarks i) Comparison of Volumes 2) The CP Principle 3) Applications I 4) Further Applications 4bis) Isolated Singularities 5 6 7 8 9 i0 ii 12 13 14 15 The Touching Principle Monotone Symmetry (MS) Gradient Bounds from Curvature Bounds I Gradient Bounds from Curvature Bounds II Barriers by Normal Perturbation Principle of n th Order ...
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The Comparison and Tangency Principles
2013We introduce the comparison and the tangency principles that will be ones of the main tools employed in this book. They are obtained when writing locally a surface as the graph of a function z=u(x,y). Then the constancy of the mean curvature on the surface implies that u satisfies a second order partial differential equation of elliptic type.
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The Comparison Principle: Nonlinearity and Nonconvexity
2014This chapter introduces generalizations and applications of the presented approach prescribed earlier to nonlinear systems, nonconvex reachability sets and systems subjected to non-ellipsoidal constraints. The key element for these issues lies in the Comparison Principle for HJB equations which indicates schemes of approximating their complicated ...
Alexander B. Kurzhanski, Pravin Varaiya
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Comparison as a Scientific Principle
1986The foregoing considerations have shown that every new notion is in a kind of opposition to those already present, and that those already present are not uninfluenced by the new one. This leads to a comparison of the old with the new, and this comparison makes its appearance quite spontaneously even in isolated observers and thinkers.
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Comparison Principles for Semilinear Poisson PDEs
2019Chapter 10 establishes comparison principles for solutions of partial differential equations. The prototypical result says that the solution of Poisson's equation gets bigger in an integral sense when the data in the equation is rearranged. Such comparisons have been used in the literature for deriving sharp bounds on certain eigenvalues, obtaining a ...
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Alternative Tax Principles: A Numerical Comparison
1993This chapter supplements the theoretical analysis of alternative tax principles by comparing the effects of tax rate differentials under the restricted destination principle and the restricted origin principle in a numerical setting. Empirical studies of cross-border shopping under pre-1993 conditions have been mentioned in Chapter 1.
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Metric Entropy and the Comparison Principle
1995Let (T, ρ) be a metric† space, e > 0. A subset S ⊂ T is called the e-net for T if, for any t ∈ T, there exists s ⊂ S such that ρ (s, t) ≤ e. In other words, T may be covered by the balls of radius e centered at points of S. Denote by N (T, e) the least possible number of points in an e-net for the set T.
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A discrete comparison principle for the time-fractional diffusion equation
Computers and Mathematics With Applications, 2020Hu Chen, Martin Stynes
exaly