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Maximum and Comparison Principles [PDF]

, 1977
The purpose of this chapter is to provide various maximum and comparison principles for quasilinear equations which extend corresponding results in Chapter 3. We consider second order, quasilinear operators Q of the form (10.1) Qu = aij(x, u, Du)Diju + b(x, u, Du), aij = aji, where x = (x1..., xn) is contained in a domain Ω of ℝn, n ≥ 2, and, unless ...
David Gilbarg, Neil S. Trudinger
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A Comparison Principle and the Lipschitz Continuity for Minimizers

2001
The authors are interested in the minimizing problem \(\int_{\Omega} L(x,u,\nabla u) \,dx \to \min\) on \(\bar{u}+W^{1,q}_{0}(\Omega)\), \(L(x,z,p)\): \(\Omega \times \mathbb{R}\times \mathbb{R}^{n}\to \mathbb{R}\). Imposing only very weak assumptions (for instance no growth conditions and no differentiability properties on \(L\) are imposed), they ...
MARICONDA, CARLO, TREU, GIULIA
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A Comparison of the Paris Principles and the International Cataloguing Principles

Cataloging & Classification Quarterly, 2009
After more than forty-five years of cataloging experience with the Paris Principles and their impact on the international sharing of bibliographic data, the process of replacing them with a wider and deeper set of International Cataloguing Principles has been completed. This article compares the scope, technological context, process of decision making,
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Comparison of Principles and Practices of Study

The School Review, 1936
Academic achievement is largely dependent on the skill with which a person handles the techniques of study. He is compelled to use these procedures and devices if he would be efficient in scholastic endeavors whether in or out of school. His whole academic life turns about this pivotal point.
C. O. Mathews, Nora Toepfer
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Elastography: history, principles, and technique comparison

Abdominal Imaging, 2015
Elastography is a relatively new imaging technology that creates images of tissue stiffness. It can be thought of an extension of the ancient technique of palpation but it gives better spatial localization information and is less subjective. Two main types of elastography are currently in use, strain elastography where the tissue displacement in ...
Brian S. Garra, Brian S. Garra
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The Comparison Principle: Nonlinearity and Nonconvexity

2014
This 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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The Comparison and Tangency Principles

2013
We 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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Comparison as a Scientific Principle

1986
The 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 in capillarity

1988
Introductory 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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Finite time stability and comparison principles

Mathematical Proceedings of the Cambridge Philosophical Society, 1968
Motivated by discussion on practical stability in LaSalle and Lefschetz (3), Weiss and Infante (5), have discussed various notions of stability over finite time interval of a given differential system. This theory of stability differs from the usual stability theory mainly by the preassigned limits to which any given solution of the differential system
J. S. W. Wong, A. A. Kayande
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