An Introduction to Maximum Principles and Symmetry in Elliptic Problems

By L. Fraenkel. 2000

311 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fa4b269c18be85b65ae7b3ced6209f43bd0b0745

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Symmetrization in geometry (2016, background): “See, for example, [2, 6, 14, 15, 16, 17, 19, 20, 30], and the references given in these texts.”
Symmetry of steady periodic surface water waves with vorticity (2004, background): “8, s ub je ct to th e Ca m br id ge C or e te rm s of u se , a va ila bl e at h tt ps :// w w w .c am br id ge .o rg /c or e/ te rm s. Assertions (i) and (ii) are respectively the Weak and the Hopf Maximum Principle, whereas (iii) is a version of the Edge Point Lemma proved in Fraenkel (2000).”
Symmetrization and Mass Comparison for Degenerate Nonlinear Parabolic and Related Elliptic Equations (2005, methodology): “Higher order equations have been treated recently treated by Ferone and Kawohl [FK].”
Characterization of balls by Riesz-potentials (2009, unknown): “Theorem 1 (Fraenkel, 2000).”
Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity (2000, background): “A virtually equivalent statement can be mathematically proved, with rigour, by combining the theorem of Caffarelli & Friedman (1980) with that of Fraenkel (1999) (theorem 4.2 and exercise 4.20).”
Degenerate bifurcation of the rotating patches (2015, methodology): “The first one is Rankine vortices where the boundary is a circle and this provides the only stationary patches according to Fraenkel’s result [13].”
Analyticity of periodic traveling free surface water waves with vorticity (2011, unknown): “Then hq(q0, 0) = 0, whereas hp(q0, 0) > 0 by Hopf’s maximum principle [11].”
Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis (2008, background): “Then zz + 2 2 XX = −a − b > 0 in D0, and since (X0, 0) = 0 = inf (X,z)∈D0 { (X, z)}, the strong maximum principle (Fraenkel, 2000) does not allow for z(X0, 0) = 0.”